Marian Anghel - Academia.edu (original) (raw)
Papers by Marian Anghel
Siam Journal on Applied Dynamical Systems, 2021
A theoretical framework which unifies the conventional Mori-Zwanzig formalism and the approximate... more A theoretical framework which unifies the conventional Mori-Zwanzig formalism and the approximate Koopman learning of deterministic dynamical systems from noiseless observation is presented. In this framework, the Mori-Zwanzig formalism, developed in statistical mechanics to tackle the hard problem of construction of reducedorder dynamics for high-dimensional dynamical systems, can be considered as a natural generalization of the Koopman description of the dynamical system. We next show that similar to the approximate Koopman learning methods, data-driven methods can be developed for the Mori-Zwanzig formalism with Mori's linear projection operator. We have developed two algorithms to extract the key operators, the Markov and the memory kernel, using time series of a reduced set of observables in a dynamical system. We have adopted the Lorenz '96 system as a test problem and solved for the above operators. These operators exhibit complex behaviors, which are unlikely to be captured by traditional modeling approaches in Mori-Zwanzig analysis. The nontrivial Generalized Fluctuation Dissipation relationship, which relates the memory kernel with the two-time correlation statistics of the orthogonal dynamics, was numerically verified as a validation of the solved operators. We present numerical evidence that the Generalized Langevin Equation, a key construct in the Mori-Zwanzig formalism, is more advantageous in predicting the evolution of the reduced set of observables than the conventional approximate Koopman operators.
Nature Physics, Dec 7, 2018
In the version of this News & Views originally published, the word 'generally' in the standfirst ... more In the version of this News & Views originally published, the word 'generally' in the standfirst was incorrectly written as 'egenerally'. This has now been corrected.
Frontiers in Environmental Science, Oct 11, 2019
We present a generalized hybrid Monte Carlo (gHMC) method for fast, statistically optimal reconst... more We present a generalized hybrid Monte Carlo (gHMC) method for fast, statistically optimal reconstruction of release histories of reactive contaminants. The approach is applicable to large-scale, strongly nonlinear systems with parametric uncertainties and data corrupted by measurement errors. The use of discrete adjoint equations facilitates numerical implementation of gHMC without putting any restrictions on the degree of nonlinearity of advection-dispersion-reaction equations that are used to describe contaminant transport in the subsurface. To demonstrate the salient features of the proposed algorithm, we identify the spatial extent of a distributed source of contamination from concentration measurements of a reactive solute.
We introduce a stochastic model that describes the quasi-static dynamics of an electric transmiss... more We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times for the failed components, and random response times to implement optimal system corrections for removing line overloads in a damaged or stressed transmission network. We use a linear approximation to the network flow equations and apply linear programming techniques that optimize the dispatching of generators and loads in order to eliminate the network overloads associated with a damaged system. We also provide a simple model for the operator's response to various contingency events that is not always optimal due to either failure of the state estimation system or due to the incorrect subjective assessment of the severity associated with these events. This further allows us to use a game theoretic framework for casting the optimization of the operator's response into the choice of the optimal strategy which minimizes the operating cost. We use a simple strategy space which is the degree of tolerance to line overloads and which is an automatic control (optimization) parameter that can be adjusted to trade off automatic load shed without propagating cascades versus reduced load shed and an increased risk of propagating cascades. The tolerance parameter is chosen to describes a smooth transition from a risk averse to a risk taken strategy. We present numerical results comparing the responses of two power grid systems to optimization approaches with different factors of risk and select the best blackout controlling parameter.
Journal of Chemical Physics, Apr 8, 2004
For two methods commonly used to achieve canonical-ensemble sampling in a molecular-dynamics simu... more For two methods commonly used to achieve canonical-ensemble sampling in a molecular-dynamics simulation, the Langevin thermostat and the Andersen [H. C. Andersen, J. Chem. Phys. 72, 2384 (1980)] thermostat, we observe, as have others, synchronization of initially independent trajectories in the same potential basin when the same random number sequence is employed. For the first time, we derive the time dependence of this synchronization for a harmonic well and show that the rate of synchronization is proportional to the thermostat coupling strength at weak coupling and inversely proportional at strong coupling with a peak in between. Explanations for the synchronization and the coupling dependence are given for both thermostats. Observation of the effect for a realistic 97-atom system indicates that this phenomenon is quite general. We discuss some of the implications of this effect and propose that it can be exploited to develop new simulation techniques. We give three examples: efficient thermalization (a concept which was also noted by Fahy and Hamann [S. Fahy and D. R. Hamann, Phys. Rev. Lett. 69, 761 (1992)]), time-parallelization of a trajectory in an infrequent-event system, and detecting transitions in an infrequent-event system.
Motivation Inference problems in classical dynamical systems Adjoint-state methods Machine learni... more Motivation Inference problems in classical dynamical systems Adjoint-state methods Machine learning using time series data Backpropagation Preliminary results: your feedback and criticism are welcomed! Tutorial-like
AGU Fall Meeting Abstracts, Dec 1, 2002
ABSTRACT We extend our numerical simulations of the discrete models of Ben-Zion and Rice (1993) a... more ABSTRACT We extend our numerical simulations of the discrete models of Ben-Zion and Rice (1993) and Ben-Zion (1996) for a cellular strike-slip fault zone in a 3D elastic solid in an effort to provide a quantitative description of the dynamical role played by various distributions of fault heterogeneity. Previous analytical results have shown that the model has an underlying critical point at zero dynamic weakening and numerical simulations indicated that a realistic description of fault instabilities should include heterogeneities which cover a wide range of size scales. In the present work we investigate disorder models that probe various generic properties of heterogeneous distributions of brittle fault properties: spatial variability (uncorrelated versus correlated Gaussian, exponential, or power-law distributions), amplitude, and anisotropy. Our extensive numerical simulations suggest that the degree of disorder in fault heterogeneities is another tuning parameter of the dynamics. As we change the disorder model, we characterize their dynamical role by measuring the change in the spatio-temporal correlation lengths of stress and seismicity fluctuations, and the power-law range of the frequency-size event statistics. Using a phase space analysis of the dynamics, we estimate the effective dimensionality of the fault models and measure how changes in the model parameters affect their dimensionality. We also determine the empirical eigenfunctions and eigenvalues generated by the dynamics of each model by using the proper orthogonal decomposition (POD). In order to extract information on the attractor of each disorder model, we analyze the time histories and phase space projections of the modal coefficients that provide a representation of the surface deformation fields in terms of the empirical eigenfunctions. This information is used to derive low-dimensional models for the dynamics and to examine its predictability as a function of the model location in the phase space of disorder models.
AGUSM, May 1, 2001
Numerical simulations of slip along a 2D cellular fault zone in a 3D elastic half-space are perfo... more Numerical simulations of slip along a 2D cellular fault zone in a 3D elastic half-space are performed for several models [Ben-Zion and Rice, 1993; Ben-Zion, 1996] that belong to a generalized phase space of models. Each model consists of a planar computational grid with uniform cells where slip is governed by brittle and creep processes, surrounded by regions with constant slip rate representing the tectonic loading. Brittle failures are governed by a static/kinetic friction law with spatially varying coefficients chosen to represent different cases of quenched heterogeneities. The creep process is given by a power law dependency of creep velocity on stress with spatially varying coefficients chosen to produce, when activated, gradual (brittle-ductile type) stress transitions at the edges of the computational grid. Quasi-static stress transfer due to slip anywhere on the fault is calculated with 3D elastic dislocation theory. Inertial effects during brittle failures are accounted for approximately by a dynamic overshoot coefficient. The phase space of models is described by generalized coordinates that measure: a) the form of slip transitions at the edges of the computational grid (we employ two different limits, one in which the creep process in the computational grid is deactivated leading to abrupt transitions, and one with gradual transitions), b) the dynamic weakening, c) the distribution of brittle fault properties, d) the fault aspect ratio, e) the depth dependence of the static friction (we simulate two different limits, one in which the static friction does not have a trend with depth and one in which it grows linearly with depth). We analyze the interplay between temporal chaos and spatial scales in the simulated patterns by measuring various quantifiers of the chaotic dynamics (such as Lyapunov exponents, entropies and dimensions of the attractor describing the motion) as we explore the phase space of models. A key tool in the analysis of the results is the proper orthogonal decomposition (POD) that determines the empirical eigenfunction and eigenvalues generated by the dynamics of each model. In order to extract information on the attractor(s) of each model we analyze the time histories and phase plane projections of the modal coefficients that provide a representation of the slip and stress fields in terms of the empirical eigenfunction. We will describe results on the use of the POD to determine the interacting active modes, to derive low-dimensional models for the dynamics, and to examine the predictability problem as a function of the model location in the phase space of fault models.
Some of the most striking features of the tectonic processes involved in faulting and earthquake ... more Some of the most striking features of the tectonic processes involved in faulting and earthquake dynamics are randomness, disorder and fault interactions. Another relevant aspect concerns the presence of ubiquitous fractal distributions characterizing the earthquake dynamics and fault morphology, suggesting that faulting and earthquake dynamics are dynamical critical phenomena. The classification of different dynamical models into universality classes and the identification of the parameters that determine their class membership will greatly enhance our understanding of these processes. In this thesis a one-dimensional fault model which incorporates shear strength and healing distance disorder, dissipation and long range interactions, is examined to elucidate the role played by randomness, disorder and interaction in this classification. Three major results are presented in this thesis. First, we use the transient regime of the fault dynamics in order to compute the critical exponents that characterize the steady-state fault dynamics and we present the first description of a disorder induced critical scaling in the transient regime. The power law exponents depend on the amount of disorder and their values saturate in the high disorder limit. Second, we present scaling arguments indicating that the underlying origin of the power law statistics present in the model can be understood quantitatively in terms of proximity to a specific non-equilibrium dynamical critical point, describing the pinning-depinning transition characteristic of driven interfaces in random media. The amount of stress dissipation present in the model controls the distance of the system from the critical point and determines the size of the critical scaling regime. Third, we show that the steady-state critical exponents do not change with the amount of healing distance disorder. The healing disorder only controls the size of the critical region. In the presence of any nonzero amount of healing disorder the shear strength disorder proves to be irrelevant in the steady-state dynamics. The system has two fixed points: a trivial limit cycle for zero disorder and a nontrivial critical disorder fixed point. The results provide a framework for expanding this research to include both morphological randomness and fault interaction and to analyze crossover effects and dynamical phase diagrams, as we change the relative importance of morphology and interaction.
arXiv (Cornell University), Jul 2, 2007
We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamica... more We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, e.g., that support vector machines (SVMs) using Gaussian RBF kernels can learn the best forecaster from a sequence of noisy observations if a) the unknown observational noise processes is bounded and has a summable alpha-mixing rate and b) the unknown ergodic dynamical system is defined by a Lipschitz continuous function on some compact subset of R^d and has a summable decay of correlations for Lipschitz continuous functions. In order to prove this result we first establish a general consistency result for SVMs and all stochastic processes that satisfy a mixing notion that is substantially weaker than alpha-mixing.
AGUFM, Dec 1, 2001
We analyze quantitatively the dynamic behavior of a class of models (Ben-Zion and Rice [1]) of a ... more We analyze quantitatively the dynamic behavior of a class of models (Ben-Zion and Rice [1]) of a discrete heterogeneous strike-slip fault system in a 3D elastic half-space, using Artificial Neural Networks (ANNs). A given model realization is characterized by a set of parameters that describe the dynamics, rheology, property disorder and fault geometry. The experimental data from the system come
International Journal for Numerical Methods in Engineering, Mar 15, 2017
Advances in nondestructive material characterization are providing a wealth of information that c... more Advances in nondestructive material characterization are providing a wealth of information that could be exploited to gain insight into general aspects of material performance and, in particular, discover relationships between microstructure and thermo-mechanical properties in polycrystalline and other complex composite materials. In order to facilitate the integration of such measurements into existing models, as well as inform new physics-based predictions, we developed a C++/MPI computational framework for sensitivity analysis and parameter estimation. The framework utilizes a micro-mechanical modeling based on fast Fourier transforms, direct and adjoint formulations, and Markov chain Monte Carlo sampling techniques. We illustrate the characteristics of this framework and demonstrate its utility by computing the residual stresses arising from thermal expansion of an elastic composite and using data from simulated experiments. We show that the availability of nondestructive 3-D measurements is crucial to reduce the uncertainty in predictions, emphasizing the importance of an integrated experimental/modeling/data analysis approach for improved material characterization and design.
Tectonophysics, Feb 1, 2006
While the top-down engineered CMOS technology favors regular and locally interconnected structure... more While the top-down engineered CMOS technology favors regular and locally interconnected structures, emerging molecular and nanoscale bottom-up self-assembled devices will be built from vast numbers of simple, densely arranged components that exhibit high failure rates, are relatively slow, and connected in a disordered way. Such systems are not programmable by standard means. Here we provide a solution to the supervised
Annals of Statistics, Apr 1, 2009
We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamica... more We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, for example, that support vector machines (SVMs) using Gaussian RBF kernels can learn the best forecaster from a sequence of noisy observations if (a) the unknown observational noise process is bounded and has a summable α-mixing rate and (b) the unknown ergodic dynamical system is defined by a Lipschitz continuous function on some compact subset of R d and has a summable decay of correlations for Lipschitz continuous functions. In order to prove this result we first establish a general consistency result for SVMs and all stochastic processes that satisfy a mixing notion that is substantially weaker than α-mixing.
Computing in Science and Engineering, 2000
Page 1. Numerical modeling of earthquake processes has become an important proving ground for ide... more Page 1. Numerical modeling of earthquake processes has become an important proving ground for ideas that have no other experimental arena. Nearly all earthquakes originate more than 10 km un-derground, making seismic ...
OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information), May 29, 2012
Siam Journal on Applied Dynamical Systems, 2021
A theoretical framework which unifies the conventional Mori-Zwanzig formalism and the approximate... more A theoretical framework which unifies the conventional Mori-Zwanzig formalism and the approximate Koopman learning of deterministic dynamical systems from noiseless observation is presented. In this framework, the Mori-Zwanzig formalism, developed in statistical mechanics to tackle the hard problem of construction of reducedorder dynamics for high-dimensional dynamical systems, can be considered as a natural generalization of the Koopman description of the dynamical system. We next show that similar to the approximate Koopman learning methods, data-driven methods can be developed for the Mori-Zwanzig formalism with Mori's linear projection operator. We have developed two algorithms to extract the key operators, the Markov and the memory kernel, using time series of a reduced set of observables in a dynamical system. We have adopted the Lorenz '96 system as a test problem and solved for the above operators. These operators exhibit complex behaviors, which are unlikely to be captured by traditional modeling approaches in Mori-Zwanzig analysis. The nontrivial Generalized Fluctuation Dissipation relationship, which relates the memory kernel with the two-time correlation statistics of the orthogonal dynamics, was numerically verified as a validation of the solved operators. We present numerical evidence that the Generalized Langevin Equation, a key construct in the Mori-Zwanzig formalism, is more advantageous in predicting the evolution of the reduced set of observables than the conventional approximate Koopman operators.
Nature Physics, Dec 7, 2018
In the version of this News & Views originally published, the word 'generally' in the standfirst ... more In the version of this News & Views originally published, the word 'generally' in the standfirst was incorrectly written as 'egenerally'. This has now been corrected.
Frontiers in Environmental Science, Oct 11, 2019
We present a generalized hybrid Monte Carlo (gHMC) method for fast, statistically optimal reconst... more We present a generalized hybrid Monte Carlo (gHMC) method for fast, statistically optimal reconstruction of release histories of reactive contaminants. The approach is applicable to large-scale, strongly nonlinear systems with parametric uncertainties and data corrupted by measurement errors. The use of discrete adjoint equations facilitates numerical implementation of gHMC without putting any restrictions on the degree of nonlinearity of advection-dispersion-reaction equations that are used to describe contaminant transport in the subsurface. To demonstrate the salient features of the proposed algorithm, we identify the spatial extent of a distributed source of contamination from concentration measurements of a reactive solute.
We introduce a stochastic model that describes the quasi-static dynamics of an electric transmiss... more We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times for the failed components, and random response times to implement optimal system corrections for removing line overloads in a damaged or stressed transmission network. We use a linear approximation to the network flow equations and apply linear programming techniques that optimize the dispatching of generators and loads in order to eliminate the network overloads associated with a damaged system. We also provide a simple model for the operator's response to various contingency events that is not always optimal due to either failure of the state estimation system or due to the incorrect subjective assessment of the severity associated with these events. This further allows us to use a game theoretic framework for casting the optimization of the operator's response into the choice of the optimal strategy which minimizes the operating cost. We use a simple strategy space which is the degree of tolerance to line overloads and which is an automatic control (optimization) parameter that can be adjusted to trade off automatic load shed without propagating cascades versus reduced load shed and an increased risk of propagating cascades. The tolerance parameter is chosen to describes a smooth transition from a risk averse to a risk taken strategy. We present numerical results comparing the responses of two power grid systems to optimization approaches with different factors of risk and select the best blackout controlling parameter.
Journal of Chemical Physics, Apr 8, 2004
For two methods commonly used to achieve canonical-ensemble sampling in a molecular-dynamics simu... more For two methods commonly used to achieve canonical-ensemble sampling in a molecular-dynamics simulation, the Langevin thermostat and the Andersen [H. C. Andersen, J. Chem. Phys. 72, 2384 (1980)] thermostat, we observe, as have others, synchronization of initially independent trajectories in the same potential basin when the same random number sequence is employed. For the first time, we derive the time dependence of this synchronization for a harmonic well and show that the rate of synchronization is proportional to the thermostat coupling strength at weak coupling and inversely proportional at strong coupling with a peak in between. Explanations for the synchronization and the coupling dependence are given for both thermostats. Observation of the effect for a realistic 97-atom system indicates that this phenomenon is quite general. We discuss some of the implications of this effect and propose that it can be exploited to develop new simulation techniques. We give three examples: efficient thermalization (a concept which was also noted by Fahy and Hamann [S. Fahy and D. R. Hamann, Phys. Rev. Lett. 69, 761 (1992)]), time-parallelization of a trajectory in an infrequent-event system, and detecting transitions in an infrequent-event system.
Motivation Inference problems in classical dynamical systems Adjoint-state methods Machine learni... more Motivation Inference problems in classical dynamical systems Adjoint-state methods Machine learning using time series data Backpropagation Preliminary results: your feedback and criticism are welcomed! Tutorial-like
AGU Fall Meeting Abstracts, Dec 1, 2002
ABSTRACT We extend our numerical simulations of the discrete models of Ben-Zion and Rice (1993) a... more ABSTRACT We extend our numerical simulations of the discrete models of Ben-Zion and Rice (1993) and Ben-Zion (1996) for a cellular strike-slip fault zone in a 3D elastic solid in an effort to provide a quantitative description of the dynamical role played by various distributions of fault heterogeneity. Previous analytical results have shown that the model has an underlying critical point at zero dynamic weakening and numerical simulations indicated that a realistic description of fault instabilities should include heterogeneities which cover a wide range of size scales. In the present work we investigate disorder models that probe various generic properties of heterogeneous distributions of brittle fault properties: spatial variability (uncorrelated versus correlated Gaussian, exponential, or power-law distributions), amplitude, and anisotropy. Our extensive numerical simulations suggest that the degree of disorder in fault heterogeneities is another tuning parameter of the dynamics. As we change the disorder model, we characterize their dynamical role by measuring the change in the spatio-temporal correlation lengths of stress and seismicity fluctuations, and the power-law range of the frequency-size event statistics. Using a phase space analysis of the dynamics, we estimate the effective dimensionality of the fault models and measure how changes in the model parameters affect their dimensionality. We also determine the empirical eigenfunctions and eigenvalues generated by the dynamics of each model by using the proper orthogonal decomposition (POD). In order to extract information on the attractor of each disorder model, we analyze the time histories and phase space projections of the modal coefficients that provide a representation of the surface deformation fields in terms of the empirical eigenfunctions. This information is used to derive low-dimensional models for the dynamics and to examine its predictability as a function of the model location in the phase space of disorder models.
AGUSM, May 1, 2001
Numerical simulations of slip along a 2D cellular fault zone in a 3D elastic half-space are perfo... more Numerical simulations of slip along a 2D cellular fault zone in a 3D elastic half-space are performed for several models [Ben-Zion and Rice, 1993; Ben-Zion, 1996] that belong to a generalized phase space of models. Each model consists of a planar computational grid with uniform cells where slip is governed by brittle and creep processes, surrounded by regions with constant slip rate representing the tectonic loading. Brittle failures are governed by a static/kinetic friction law with spatially varying coefficients chosen to represent different cases of quenched heterogeneities. The creep process is given by a power law dependency of creep velocity on stress with spatially varying coefficients chosen to produce, when activated, gradual (brittle-ductile type) stress transitions at the edges of the computational grid. Quasi-static stress transfer due to slip anywhere on the fault is calculated with 3D elastic dislocation theory. Inertial effects during brittle failures are accounted for approximately by a dynamic overshoot coefficient. The phase space of models is described by generalized coordinates that measure: a) the form of slip transitions at the edges of the computational grid (we employ two different limits, one in which the creep process in the computational grid is deactivated leading to abrupt transitions, and one with gradual transitions), b) the dynamic weakening, c) the distribution of brittle fault properties, d) the fault aspect ratio, e) the depth dependence of the static friction (we simulate two different limits, one in which the static friction does not have a trend with depth and one in which it grows linearly with depth). We analyze the interplay between temporal chaos and spatial scales in the simulated patterns by measuring various quantifiers of the chaotic dynamics (such as Lyapunov exponents, entropies and dimensions of the attractor describing the motion) as we explore the phase space of models. A key tool in the analysis of the results is the proper orthogonal decomposition (POD) that determines the empirical eigenfunction and eigenvalues generated by the dynamics of each model. In order to extract information on the attractor(s) of each model we analyze the time histories and phase plane projections of the modal coefficients that provide a representation of the slip and stress fields in terms of the empirical eigenfunction. We will describe results on the use of the POD to determine the interacting active modes, to derive low-dimensional models for the dynamics, and to examine the predictability problem as a function of the model location in the phase space of fault models.
Some of the most striking features of the tectonic processes involved in faulting and earthquake ... more Some of the most striking features of the tectonic processes involved in faulting and earthquake dynamics are randomness, disorder and fault interactions. Another relevant aspect concerns the presence of ubiquitous fractal distributions characterizing the earthquake dynamics and fault morphology, suggesting that faulting and earthquake dynamics are dynamical critical phenomena. The classification of different dynamical models into universality classes and the identification of the parameters that determine their class membership will greatly enhance our understanding of these processes. In this thesis a one-dimensional fault model which incorporates shear strength and healing distance disorder, dissipation and long range interactions, is examined to elucidate the role played by randomness, disorder and interaction in this classification. Three major results are presented in this thesis. First, we use the transient regime of the fault dynamics in order to compute the critical exponents that characterize the steady-state fault dynamics and we present the first description of a disorder induced critical scaling in the transient regime. The power law exponents depend on the amount of disorder and their values saturate in the high disorder limit. Second, we present scaling arguments indicating that the underlying origin of the power law statistics present in the model can be understood quantitatively in terms of proximity to a specific non-equilibrium dynamical critical point, describing the pinning-depinning transition characteristic of driven interfaces in random media. The amount of stress dissipation present in the model controls the distance of the system from the critical point and determines the size of the critical scaling regime. Third, we show that the steady-state critical exponents do not change with the amount of healing distance disorder. The healing disorder only controls the size of the critical region. In the presence of any nonzero amount of healing disorder the shear strength disorder proves to be irrelevant in the steady-state dynamics. The system has two fixed points: a trivial limit cycle for zero disorder and a nontrivial critical disorder fixed point. The results provide a framework for expanding this research to include both morphological randomness and fault interaction and to analyze crossover effects and dynamical phase diagrams, as we change the relative importance of morphology and interaction.
arXiv (Cornell University), Jul 2, 2007
We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamica... more We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, e.g., that support vector machines (SVMs) using Gaussian RBF kernels can learn the best forecaster from a sequence of noisy observations if a) the unknown observational noise processes is bounded and has a summable alpha-mixing rate and b) the unknown ergodic dynamical system is defined by a Lipschitz continuous function on some compact subset of R^d and has a summable decay of correlations for Lipschitz continuous functions. In order to prove this result we first establish a general consistency result for SVMs and all stochastic processes that satisfy a mixing notion that is substantially weaker than alpha-mixing.
AGUFM, Dec 1, 2001
We analyze quantitatively the dynamic behavior of a class of models (Ben-Zion and Rice [1]) of a ... more We analyze quantitatively the dynamic behavior of a class of models (Ben-Zion and Rice [1]) of a discrete heterogeneous strike-slip fault system in a 3D elastic half-space, using Artificial Neural Networks (ANNs). A given model realization is characterized by a set of parameters that describe the dynamics, rheology, property disorder and fault geometry. The experimental data from the system come
International Journal for Numerical Methods in Engineering, Mar 15, 2017
Advances in nondestructive material characterization are providing a wealth of information that c... more Advances in nondestructive material characterization are providing a wealth of information that could be exploited to gain insight into general aspects of material performance and, in particular, discover relationships between microstructure and thermo-mechanical properties in polycrystalline and other complex composite materials. In order to facilitate the integration of such measurements into existing models, as well as inform new physics-based predictions, we developed a C++/MPI computational framework for sensitivity analysis and parameter estimation. The framework utilizes a micro-mechanical modeling based on fast Fourier transforms, direct and adjoint formulations, and Markov chain Monte Carlo sampling techniques. We illustrate the characteristics of this framework and demonstrate its utility by computing the residual stresses arising from thermal expansion of an elastic composite and using data from simulated experiments. We show that the availability of nondestructive 3-D measurements is crucial to reduce the uncertainty in predictions, emphasizing the importance of an integrated experimental/modeling/data analysis approach for improved material characterization and design.
Tectonophysics, Feb 1, 2006
While the top-down engineered CMOS technology favors regular and locally interconnected structure... more While the top-down engineered CMOS technology favors regular and locally interconnected structures, emerging molecular and nanoscale bottom-up self-assembled devices will be built from vast numbers of simple, densely arranged components that exhibit high failure rates, are relatively slow, and connected in a disordered way. Such systems are not programmable by standard means. Here we provide a solution to the supervised
Annals of Statistics, Apr 1, 2009
We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamica... more We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, for example, that support vector machines (SVMs) using Gaussian RBF kernels can learn the best forecaster from a sequence of noisy observations if (a) the unknown observational noise process is bounded and has a summable α-mixing rate and (b) the unknown ergodic dynamical system is defined by a Lipschitz continuous function on some compact subset of R d and has a summable decay of correlations for Lipschitz continuous functions. In order to prove this result we first establish a general consistency result for SVMs and all stochastic processes that satisfy a mixing notion that is substantially weaker than α-mixing.
Computing in Science and Engineering, 2000
Page 1. Numerical modeling of earthquake processes has become an important proving ground for ide... more Page 1. Numerical modeling of earthquake processes has become an important proving ground for ideas that have no other experimental arena. Nearly all earthquakes originate more than 10 km un-derground, making seismic ...
OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information), May 29, 2012