Hector Klie - Academia.edu (original) (raw)
Papers by Hector Klie
Proceedings, Sep 8, 2014
igh dimensional. The present work describes an efficient optimization methodology for black-box s... more igh dimensional. The present work describes an efficient optimization methodology for black-box simulations consisting of inferring and calibrating a “twin model” representation of the black-box simulator. The twin model is a non-intrusive model that mirrors the behavior of the black-box simulation using data assimilation techniques. Once the inferred twin model is available, adjoint operators based on gradient-driven techniques can be easily computed to perform efficient optimization. Computational experiments illustrate the significant reduction of simulations to estimate the optimal water injection strategy under various geological uncertainty scenarios when compared with traditional approaches using gradient-free methods.
We propose a novel learning optimization approach to find nearly optimal field solutions with a h... more We propose a novel learning optimization approach to find nearly optimal field solutions with a high probability and at a relatively low computational expense. Key attributes of the approach include capabilities to handle non-linear constraints in a dynamic fashion, automatic control of search directions; use of machine learning-based proxies; real time control of the optimization execution flow and, risk management decisions. The resulting algorithm retains the attractive property that the number of simulations is independent of the number of decision parameters as it progressively improves its rate of convergence as more information becomes available. We illustrate the new approach to determine multiple well locations and operation strategies to optimize field production on deep water and unconventional resource applications.
12th European Conference on the Mathematics of Oil Recovery, Sep 6, 2010
The premise of the present work lies on the fact that a large number of system coefficients may b... more The premise of the present work lies on the fact that a large number of system coefficients may be disregarded without compromising the robustness of the overall solution process. That is, given a linear system it is possible to construct a preconditioner by dropping a large number of off-diagonal nonzeros and use it as a suitable proxy to approximate the original matrix. This proxy system can be in turn factored to generate a new class of block ILU preconditioners, approximated inverses and algebraic multigrid implementations. We propose two parallel algorithms to sparsify a given linear system: (a) random sampling sparsification (RSS), and (b) percolation-based sparsification (PBS). The former one relies on the idea that coefficients are included into the sparsified system with a probability proportional to its effective transmissibility. The latter relies on capturing highly connected flow paths described by whole set of transmissibility coefficients. Depending on the case, the RSS and PS algorithms have the potential to reduce in orders of magnitude the number of floating point operations associated with the preconditioner. Results confirming the benefits of sparsified solvers are illustrated on a wide set of field cases arising in black-oil and compositional simulations.
All Days, Feb 18, 2013
The present paper proposes a novel non-intrusive model reduction approach based on Proper Orthogo... more The present paper proposes a novel non-intrusive model reduction approach based on Proper Orthogonal Decomposition (POD), the Discrete Empirical Interpolation Method (DEIM) and Radial Basis Function (RBF) networks to efficiently predict production of oil and gas reservoirs. Provided a representative set of training reservoir scenarios, either POD or DEIM allows for effectively projecting input parameters (e.g., permeability, porosity), states (e.g., pressure, saturations) and outputs (e.g., well production curves) into a much lower dimension that retains the main features contained in the simulation system. In this work, these projections are applied across multiple levels to be able to collapse a large number of spatio-temporal correlations. It is observed that these projections can be effectively performed at a large extent regardless of the underlying geological complexity and operational constraints associated with the reservoir model. The RBF network provides a powerful means for developing learning functions from input-output relationships described by the reservoir dynamics entailed by multiple combinations of inputs and controls. In order to achieve a high degree of predictability from the resulting reduced model, the RBF network exploits locality by a means of Gaussian basis functions that are maximal at the sampled point and decrease monotonically with distance. Compared to multilayer perceptron networks (i.e., traditional artificial neural networks) RBF networks require less training and are less sensitive to the presence of noise in the data. In this regard, POD or DEIM acts as a data filter that additionally aids at designing a more compact RBF network representation suitable for targeting fast reservoir predictions. Numerical results show significant accelerations with respect to running the original simulation model on a set of field-motivated cases.
MDPI eBooks, May 23, 2020
APS Division of Fluid Dynamics Meeting Abstracts, Nov 1, 2013
ECMOR XIII - 13th European Conference on the Mathematics of Oil Recovery, Sep 10, 2012
Thermal recovery typically entails higher costs than conventional oil recovery, so the applicatio... more Thermal recovery typically entails higher costs than conventional oil recovery, so the application of computational optimization techniques may be beneficial. Optimization, however, requires many simulations, which incurs substantial computational cost. Here we apply a model-order reduction technique, which aims at large reductions in computational requirements. The technique considered, trajectory piecewise linearization (TPWL), entails the representation of new solutions in terms of linearizations around previously simulated (and saved) training solutions. The linearized representation is projected into a low-dimensional space, with the projection matrix constructed through proper orthogonal decomposition of solution `snapshots' generated in a training step. We consider two idealized problems, specifically primary production of oil driven by downhole heaters, and a simplified model for steam assisted gravity drainage, where water and steam are treated as a single `effective' phase. The strong temperature dependence of oil viscosity is included in both cases. TPWL test-case results for these systems demonstrate that the method can provide accurate predictions relative to full-order reference solutions. The overhead associated with TPWL model construction is equivalent to the computation time for several full-order simulations (the precise overhead depends on the number of training runs). Observed runtime speedups are very substantial -- over two orders of magnitude.
AGU Fall Meeting Abstracts, Dec 1, 2019
This dissertation centers on two major aspects dictating the computational time of applications b... more This dissertation centers on two major aspects dictating the computational time of applications based on the solution of systems of coupled nonlinear parabolic equations: nonlinear and linear iterations. The former aspect leads to the conception of a novel way of reusing the Krylov information generated by GMRES for solving linear systems arising within a Newton method. The approach stems from theory recently developed on a nonlinear version of the Eirola-Nevanlinna, algorithm (originally for solving non-symmetric linear systems) which is capable of converging twice as fast as Broyden's method. A secant update strategy of the Hessenberg matrix resulting from the Arnoldi process in GMRES amounts to reflecting a secant update of the current Jacobian with the rank-one term projected onto the generated Krylov subspace (Krylov-Broyden update). This allows the design of a new nonlinear Krylov-Eirola-Nevanlinna (KEN) algorithm and a higher-order version of Newton's method (HOKN) as...
L'invention concerne generalement une infrastructure informatique parallele concue pour accel... more L'invention concerne generalement une infrastructure informatique parallele concue pour accelerer des operations intensives au niveau du noyau et faire face a une physique complexe dans des simulations de reservoir numerique en utilisant efficacement une plateforme informatique multicœur. Specifiquement, cette simulation parallele avancee multicœur (MAPS) utilise une heuristique pour determiner les configurations materielles optimales et les composants logiciels optimaux pour les caracteristiques d'un probleme donne afin de concevoir efficacement un modele.
. Two-stage procedures refers to a family of convergent nested or inner-outer iterations.This pap... more . Two-stage procedures refers to a family of convergent nested or inner-outer iterations.This paper addresses their use as preconditioners in the context of systems of coupled nonlinear partialdifferential equations, specifically those modeling underground multiphase flow phenomena. The linearsystems arising after the discretization and the Newton linearization are highly nonsymmetric andindefinite but coefficient blocks associated with a particular type of unknown
. Keywords: secant methods, Krylov subspace methods, nonlinear equations, Newton's metho... more . Keywords: secant methods, Krylov subspace methods, nonlinear equations, Newton's method, Broyden's method AMS(MOS) subject classification: 3504, 35Q35, 35M10 1. Introduction. The solution of the nonlinear system of equations F (u) = 0; (1) where F :\Omega ` IR n ! IR n , is cornerstone in many scientific and engineering applications. In not rare cases, the number of variables involved in this problem surpasses the computing capabilities today. Therefore, it is necessary not only to come up with strategies to exploit the mathematical and physical structure of the problem but also to create algorithms that resuse as much as possible the inherent information produced towrd the solution of the problem. Among several methods, Newton's method and Broyden's method have been two of the main choices to solve (1) [12, 28, 34, 35]. The former is very popular due to its robustness and well known q-quadratic local convergence. The latter is an alternative to the former when the computatio...
SEG Technical Program Expanded Abstracts 2000, 2000
All Days, 2013
The present paper proposes a novel non-intrusive model reduction approach based on Proper Orthogo... more The present paper proposes a novel non-intrusive model reduction approach based on Proper Orthogonal Decomposition (POD), the Discrete Empirical Interpolation Method (DEIM) and Radial Basis Function (RBF) networks to efficiently predict production of oil and gas reservoirs. Provided a representative set of training reservoir scenarios, either POD or DEIM allows for effectively projecting input parameters (e.g., permeability, porosity), states (e.g., pressure, saturations) and outputs (e.g., well production curves) into a much lower dimension that retains the main features contained in the simulation system. In this work, these projections are applied across multiple levels to be able to collapse a large number of spatio-temporal correlations. It is observed that these projections can be effectively performed at a large extent regardless of the underlying geological complexity and operational constraints associated with the reservoir model. The RBF network provides a powerful means f...
Proceedings, Sep 8, 2014
igh dimensional. The present work describes an efficient optimization methodology for black-box s... more igh dimensional. The present work describes an efficient optimization methodology for black-box simulations consisting of inferring and calibrating a “twin model” representation of the black-box simulator. The twin model is a non-intrusive model that mirrors the behavior of the black-box simulation using data assimilation techniques. Once the inferred twin model is available, adjoint operators based on gradient-driven techniques can be easily computed to perform efficient optimization. Computational experiments illustrate the significant reduction of simulations to estimate the optimal water injection strategy under various geological uncertainty scenarios when compared with traditional approaches using gradient-free methods.
We propose a novel learning optimization approach to find nearly optimal field solutions with a h... more We propose a novel learning optimization approach to find nearly optimal field solutions with a high probability and at a relatively low computational expense. Key attributes of the approach include capabilities to handle non-linear constraints in a dynamic fashion, automatic control of search directions; use of machine learning-based proxies; real time control of the optimization execution flow and, risk management decisions. The resulting algorithm retains the attractive property that the number of simulations is independent of the number of decision parameters as it progressively improves its rate of convergence as more information becomes available. We illustrate the new approach to determine multiple well locations and operation strategies to optimize field production on deep water and unconventional resource applications.
12th European Conference on the Mathematics of Oil Recovery, Sep 6, 2010
The premise of the present work lies on the fact that a large number of system coefficients may b... more The premise of the present work lies on the fact that a large number of system coefficients may be disregarded without compromising the robustness of the overall solution process. That is, given a linear system it is possible to construct a preconditioner by dropping a large number of off-diagonal nonzeros and use it as a suitable proxy to approximate the original matrix. This proxy system can be in turn factored to generate a new class of block ILU preconditioners, approximated inverses and algebraic multigrid implementations. We propose two parallel algorithms to sparsify a given linear system: (a) random sampling sparsification (RSS), and (b) percolation-based sparsification (PBS). The former one relies on the idea that coefficients are included into the sparsified system with a probability proportional to its effective transmissibility. The latter relies on capturing highly connected flow paths described by whole set of transmissibility coefficients. Depending on the case, the RSS and PS algorithms have the potential to reduce in orders of magnitude the number of floating point operations associated with the preconditioner. Results confirming the benefits of sparsified solvers are illustrated on a wide set of field cases arising in black-oil and compositional simulations.
All Days, Feb 18, 2013
The present paper proposes a novel non-intrusive model reduction approach based on Proper Orthogo... more The present paper proposes a novel non-intrusive model reduction approach based on Proper Orthogonal Decomposition (POD), the Discrete Empirical Interpolation Method (DEIM) and Radial Basis Function (RBF) networks to efficiently predict production of oil and gas reservoirs. Provided a representative set of training reservoir scenarios, either POD or DEIM allows for effectively projecting input parameters (e.g., permeability, porosity), states (e.g., pressure, saturations) and outputs (e.g., well production curves) into a much lower dimension that retains the main features contained in the simulation system. In this work, these projections are applied across multiple levels to be able to collapse a large number of spatio-temporal correlations. It is observed that these projections can be effectively performed at a large extent regardless of the underlying geological complexity and operational constraints associated with the reservoir model. The RBF network provides a powerful means for developing learning functions from input-output relationships described by the reservoir dynamics entailed by multiple combinations of inputs and controls. In order to achieve a high degree of predictability from the resulting reduced model, the RBF network exploits locality by a means of Gaussian basis functions that are maximal at the sampled point and decrease monotonically with distance. Compared to multilayer perceptron networks (i.e., traditional artificial neural networks) RBF networks require less training and are less sensitive to the presence of noise in the data. In this regard, POD or DEIM acts as a data filter that additionally aids at designing a more compact RBF network representation suitable for targeting fast reservoir predictions. Numerical results show significant accelerations with respect to running the original simulation model on a set of field-motivated cases.
MDPI eBooks, May 23, 2020
APS Division of Fluid Dynamics Meeting Abstracts, Nov 1, 2013
ECMOR XIII - 13th European Conference on the Mathematics of Oil Recovery, Sep 10, 2012
Thermal recovery typically entails higher costs than conventional oil recovery, so the applicatio... more Thermal recovery typically entails higher costs than conventional oil recovery, so the application of computational optimization techniques may be beneficial. Optimization, however, requires many simulations, which incurs substantial computational cost. Here we apply a model-order reduction technique, which aims at large reductions in computational requirements. The technique considered, trajectory piecewise linearization (TPWL), entails the representation of new solutions in terms of linearizations around previously simulated (and saved) training solutions. The linearized representation is projected into a low-dimensional space, with the projection matrix constructed through proper orthogonal decomposition of solution `snapshots' generated in a training step. We consider two idealized problems, specifically primary production of oil driven by downhole heaters, and a simplified model for steam assisted gravity drainage, where water and steam are treated as a single `effective' phase. The strong temperature dependence of oil viscosity is included in both cases. TPWL test-case results for these systems demonstrate that the method can provide accurate predictions relative to full-order reference solutions. The overhead associated with TPWL model construction is equivalent to the computation time for several full-order simulations (the precise overhead depends on the number of training runs). Observed runtime speedups are very substantial -- over two orders of magnitude.
AGU Fall Meeting Abstracts, Dec 1, 2019
This dissertation centers on two major aspects dictating the computational time of applications b... more This dissertation centers on two major aspects dictating the computational time of applications based on the solution of systems of coupled nonlinear parabolic equations: nonlinear and linear iterations. The former aspect leads to the conception of a novel way of reusing the Krylov information generated by GMRES for solving linear systems arising within a Newton method. The approach stems from theory recently developed on a nonlinear version of the Eirola-Nevanlinna, algorithm (originally for solving non-symmetric linear systems) which is capable of converging twice as fast as Broyden's method. A secant update strategy of the Hessenberg matrix resulting from the Arnoldi process in GMRES amounts to reflecting a secant update of the current Jacobian with the rank-one term projected onto the generated Krylov subspace (Krylov-Broyden update). This allows the design of a new nonlinear Krylov-Eirola-Nevanlinna (KEN) algorithm and a higher-order version of Newton's method (HOKN) as...
L'invention concerne generalement une infrastructure informatique parallele concue pour accel... more L'invention concerne generalement une infrastructure informatique parallele concue pour accelerer des operations intensives au niveau du noyau et faire face a une physique complexe dans des simulations de reservoir numerique en utilisant efficacement une plateforme informatique multicœur. Specifiquement, cette simulation parallele avancee multicœur (MAPS) utilise une heuristique pour determiner les configurations materielles optimales et les composants logiciels optimaux pour les caracteristiques d'un probleme donne afin de concevoir efficacement un modele.
. Two-stage procedures refers to a family of convergent nested or inner-outer iterations.This pap... more . Two-stage procedures refers to a family of convergent nested or inner-outer iterations.This paper addresses their use as preconditioners in the context of systems of coupled nonlinear partialdifferential equations, specifically those modeling underground multiphase flow phenomena. The linearsystems arising after the discretization and the Newton linearization are highly nonsymmetric andindefinite but coefficient blocks associated with a particular type of unknown
. Keywords: secant methods, Krylov subspace methods, nonlinear equations, Newton's metho... more . Keywords: secant methods, Krylov subspace methods, nonlinear equations, Newton's method, Broyden's method AMS(MOS) subject classification: 3504, 35Q35, 35M10 1. Introduction. The solution of the nonlinear system of equations F (u) = 0; (1) where F :\Omega ` IR n ! IR n , is cornerstone in many scientific and engineering applications. In not rare cases, the number of variables involved in this problem surpasses the computing capabilities today. Therefore, it is necessary not only to come up with strategies to exploit the mathematical and physical structure of the problem but also to create algorithms that resuse as much as possible the inherent information produced towrd the solution of the problem. Among several methods, Newton's method and Broyden's method have been two of the main choices to solve (1) [12, 28, 34, 35]. The former is very popular due to its robustness and well known q-quadratic local convergence. The latter is an alternative to the former when the computatio...
SEG Technical Program Expanded Abstracts 2000, 2000
All Days, 2013
The present paper proposes a novel non-intrusive model reduction approach based on Proper Orthogo... more The present paper proposes a novel non-intrusive model reduction approach based on Proper Orthogonal Decomposition (POD), the Discrete Empirical Interpolation Method (DEIM) and Radial Basis Function (RBF) networks to efficiently predict production of oil and gas reservoirs. Provided a representative set of training reservoir scenarios, either POD or DEIM allows for effectively projecting input parameters (e.g., permeability, porosity), states (e.g., pressure, saturations) and outputs (e.g., well production curves) into a much lower dimension that retains the main features contained in the simulation system. In this work, these projections are applied across multiple levels to be able to collapse a large number of spatio-temporal correlations. It is observed that these projections can be effectively performed at a large extent regardless of the underlying geological complexity and operational constraints associated with the reservoir model. The RBF network provides a powerful means f...