相关论文: A scalable matrix-free spectral element approach f…
This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…
The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and then the analysis problem is solved by solving operator-valued…
Solving partial differential equations (PDEs) numerically often requires huge computing time, energy cost, and hardware resources in practical applications. This has limited their applications in many scenarios (e.g., autonomous systems,…
Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.…
Projected Gradient Descent (PGD) methods offer a simple and scalable approach to topology optimization (TO), yet they often struggle with nonlinear and multi-constraint problems due to the complexity of active-set detection. This paper…
This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element…
Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discretization. By leveraging Gaussian process regression and…
Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…
Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…
Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have shown much promise for simulating such complex…
Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…
In this manuscript, we introduce the tensor-train reduced basis method, a novel projection-based reduced-order model designed for the efficient solution of parameterized partial differential equations. While reduced-order models are widely…
We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic…
We propose UPOQA, a derivative-free optimization algorithm for partially separable unconstrained problems, leveraging quadratic interpolation and a structured trust-region framework. By decomposing the objective into element functions,…
Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free…
A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular domains is described, based on separable representations of partial differential…
In this paper, we address the distributed prescribed-time convex optimization (DPTCO) problem for a class of nonlinear multi-agent systems (MASs) under undirected connected graph. A cascade design framework is proposed such that the DPTCO…
This paper develops and analyzes an optimal-order semi-discrete scheme and its fully discrete finite element approximation for nonlinear stochastic elastic wave equations with multiplicative noise. A non-standard time-stepping scheme is…
The solution of optimization problems constrained by partial differential equations (PDEs) plays an important role in many areas of science and industry. In this work we present cashocs, a new software package written in Python, which…
Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…