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

We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…

The advent of scientific machine learning (SciML) has opened up a new field with many promises and challenges in the field of simulation science by developing approaches at the interface of physics- and data-based modelling. To this end,…

A physics-informed neural network (PINN) models the dynamics of a system by integrating the governing physical laws into the architecture of a neural network. By enforcing physical laws as constraints, PINN overcomes challenges with data…

Physics-informed neural networks (PINNs) offer a novel AI-driven framework for integrating physical laws directly into neural network models, facilitating the solution of complex multiphysics problems in materials engineering. This study…

Visual coverage path planning with unmanned aerial vehicles (UAVs) requires agents to strategically coordinate UAV motion and camera control to maximize coverage, minimize redundancy, and maintain battery efficiency. Traditional…

We study the statistical-computational trade-offs for learning with exact invariances (or symmetries) using kernel regression. Traditional methods, such as data augmentation, group averaging, canonicalization, and frame-averaging, either…

Neural networks can emulate nonlinear physical systems with high accuracy, yet they may produce physically-inconsistent results when violating fundamental constraints. Here, we introduce a systematic way of enforcing nonlinear analytic…

Quantifier elimination (qelim) is used in many automated reasoning tasks including program synthesis, exist-forall solving, quantified SMT, Model Checking, and solving Constrained Horn Clauses (CHCs). Exact qelim is computationally…

Neural collapse is a highly symmetric geometric pattern of neural networks that emerges during the terminal phase of training, with profound implications on the generalization performance and robustness of the trained networks. To…

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

Extreme learning machine (ELM) is a new single hidden layer feedback neural network. The weights of the input layer and the biases of neurons in hidden layer are randomly generated, the weights of the output layer can be analytically…

We propose a hybrid physics-informed machine learning framework to approximate invariant manifolds (IMs) of discrete-time dynamical systems driven by exogenous autonomous dynamics (exosystems). Such systems appear in applications ranging…

Training implicit neural representations (INRs) to capture fine-scale details typically relies on iterative backpropagation and is often hindered by spectral bias when the target exhibits highly non-uniform frequency content. We propose…

Learning-based approaches, notably Reinforcement Learning (RL), have shown promise for solving optimal control tasks without explicit system models. However, these approaches are often sample-inefficient, sensitive to reward design and…

Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…

Nonlinear embedding manifold learning methods provide invaluable visual insights into the structure of high-dimensional data. However, due to a complicated nonconvex objective function, these methods can easily get stuck in local minima and…

Subspace identification methods (SIMs) have proven to be very useful and numerically robust for building state-space models. While most SIMs are consistent, few if any can achieve the efficiency of the maximum likelihood estimate (MLE).…

The semiconductor industry faces a computational crisis in extreme ultraviolet (EUV) lithography optimization, where traditional methods consume billions of CPU hours while failing to achieve sub-nanometer precision. We present a…

Physics-informed neural networks (PINNs) have plateaued at errors of $10^{-3}$-$10^{-4}$ for fourth-order partial differential equations, creating a perceived precision ceiling that limits their adoption in engineering applications. We…

Since their advent nearly a decade ago, physics-informed neural networks (PINNs) have been studied extensively as a novel technique for solving forward and inverse problems in physics and engineering. The neural network discretization of…