Related papers: Exact Constraint Enforcement in Physics-Informed E…

We present a focused introduction to exact penalty methods for nonlinear programs and mathematical programs with equilibrium constraints (MPECs), emphasizing their connection to modern error bound theory. The goal is twofold. First, we…

Physics-Informed Machine Learning (PIML) offers a powerful paradigm of integrating data with physical laws to address important scientific problems, such as parameter estimation, inferring hidden physics, equation discovery, and state…

We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…

We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal functions. We show that a feedforward neural network with a…

Ensuring neural networks adhere to domain-specific constraints is crucial for addressing safety and trustworthiness while also enhancing inference accuracy. Despite the nonlinear nature of most real-world tasks, the majority of existing…

A handy technique for the Finite Element Method (FEM) is presented that uses the null space for the implementation of Dirichlet and constraint boundary conditions. The focus of this method is to present an illustrative approach to modeling…

For Stefan problems, characterized by moving boundaries and discontinuous coefficients due to phase changes, the inherent nonconvexity of the objective functional frequently causes optimization difficulty in randomized neural network…

Physics-informed machine learning (PIML) integrates partial differential equations (PDEs) into machine learning models to solve inverse problems, such as estimating coefficient functions (e.g., the Hamiltonian function) that characterize…

In this paper, we introduce a new approach based on distance fields to exactly impose boundary conditions in physics-informed deep neural networks. The challenges in satisfying Dirichlet boundary conditions in meshfree and particle methods…

Neural networks can approximate solutions to partial differential equations, but they often break the very laws they are meant to model-creating mass from nowhere, drifting shocks, or violating conservation and entropy. We address this by…

We propose a new family of neural networks to predict the behaviors of physical systems by learning their underpinning constraints. A neural projection operator lies at the heart of our approach, composed of a lightweight network with an…

In recent years, a number of tools have become available that recover the underlying control policy from constrained movements. However, few have explicitly considered learning the constraints of the motion and ways to cope with unknown…

In theory, boundary and initial conditions are important for the wellposedness of partial differential equations (PDEs). Numerically, these conditions can be enforced exactly in classical numerical methods, such as finite difference method…

Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective…

Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some combinatorial properties of the constraints. We first propose an equivalent optimization…

Low-level C programs remain highly vulnerable to out-of-bounds memory corruption. State-of-the-art precise defenses either introduce severe runtime overhead due to metadata memory lookups, or break standard C semantics by disallowing…

This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…

We reformulate the zero-norm minimization problem as an equivalent mathematical program with equilibrium constraints and establish that its penalty problem, induced by adding the complementarity constraint to the objective, is exact. Then,…

The paper concerns optimization problems with general equality and inequality constraints and with constraints expressed by a convex set. In order to solve these problems, the general constraints are treated by an exact penalty functions…

We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…