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Showing 1 to 16 of 16 for “"PDE-constrained optimization"”.
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A certified reduced basis approach to PDE-constrained optimization
Parameter optimization problems constrained by partial differential equations (PDEs) appear in many science and engineering applications. The PDE usually describes the underlying system or component behavior, while the parameters identify a particular configurations of the component, such as …
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Efficient estimation of coherent risk measures for risk-averse optimization problems governed by partial differential equations with random inputs
… of quantities of interest in the context of optimization of partial differential equations (PDEs) with random inputs. Risk measures of the quantities of interest arise as objective functions or as constraints in the PDE-constrained optimization problems under uncertainty. A single evaluation …
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Multiscale Approach to Optimal Control of in Situ Bioremediation of Groundwater
… identified the importance of the interaction of PDE discretization and optimization. The bioremediation optimal control model is governed by a set of nonlinear PDEs (the transition equation), which describe the system response under given pumping rates. Since solving the PDEs is only a subproblem …
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Multilevel-in-Time Methods for Optimal Control of PDEs and Training of Recurrent Neural Networks
… linear-quadratic Partial Differential Equation (PDE)-constrained optimization problems and Recurrent Neural Network (RNN) training problems. While these two problem classes seem different, they share a time-like structure. The proposed methods exploit decompositions in time of the optimization …
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ADMM Based Methods for Time-Domain Decomposition Formulations of Optimal Control Problems
… linear-quadratic partial differential equation (PDE)-constrained optimization problems. The solution of such optimization problems is computing time and memory intensive. TDD formulations split the time-dependent PDE into coupled subdomain equations and introduce potential for parallelism and …
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Hessian Matrix-Free Lagrange-Newton-Krylov-Schur-Schwarz Methods for Elliptic Inverse Problems
… systems. The inverse problem is constructed as a PDE-constrained optimization, where the cost function is the <em>L</em><sup>2</sup> norm of the difference between the measured data and the predicted state variable, and the constraint is an elliptic PDE. Particular examples of the system …
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Data-driven Modeling of Lithium Intercalation Materials
… the population dynamics in a porous electrode. PDE-constrained optimization and Bayesian inference are used to infer and quantify the uncertainty of the constitutive laws from multiple data streams. Applications include learning the constitutive laws from images of pattern formation, inverting …
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Damage Detection and Sensor Placement Strategies for Structures Under Frequency-Domain Dynamics
… of discretized partial differential equations (PDEs). Abstractly, we construct and solve the corresponding (potentially nonlinear) inverse problem to attain a parameter estimator. Then, to devise the next best sensor placement, we linearize the OED problem around the newly determined estimator …
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Combustion Physics and Inverse Modeling of Energetic Materials
… material properties and chemical kinetics using PDE-constrained optimization, which allows for deciphering the reaction-transport coupling from observable dynamics in currently available combustion diagnostic tools. We further discuss training challenges of neural differential equations with data …
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Advances in Symbolic Regression: From Generalized Formulation to Density Estimation and Inverse Problem
… method that redefines the traditional SR optimization problem to discover analytical mappings from the input space to a transformed output space. The proposed GSR approach achieves promising performance compared to existing SR methods across established benchmark datasets, as well as a …
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Inverse-Problem Inspired Approaches in the Design of Solids for Frequency-Domain Dynamics
… in many engineered systems. Computational optimization methods can usefully guide the design of structures and solid systems to obtain layouts with desired dynamic behaviors, such as minimized or tailored vibration response, while accounting for additional constraints. Due to resonance …
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Density-to-Potential Inversions in Density Functional Theory
… inversion methods use classical gradient-based optimization routines that are constrained to satisfy the governing partial differential equations. Numerous examples are given to illustrate the strengths and weaknesses of the different inversion methods.
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MODEL-BASED LEARNING AND CONTROL OF ADVECTION-DIFFUSION TRANSPORT USING MOBILE ROBOTS
… particularly Partial Differential Equations (PDEs), has been hindered for many years due to the lack of adequate computational resources onboard mobile robots. One such problem of interest for the roboticists, that can hugely benefit from more descriptive models, is Chemical Plume Tracing …
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Spectral Optimization Problems Controlling Wave Phenomena
… design problems are formulated as PDE-constrained optimization problems to find the material arrangement that maximizes an objective function which expresses the desired behavior. The PDE constraint describes the relationship between the material and the phenomena of interest. The …
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A methodology for non-Intrusive projection-based model reduction of expensive black-box PDE-based systems and application in the many-query context
… work is that it converts the original non-linear PDE system into a linear PDE system with auxiliary non-linear algebraic equations which are then projected onto the POD subspace. By such a linearization, it is shown that the governing equations can be extracted by directly discretizing the linear …