Related papers: Neural operators struggle to learn complex PDEs in…

This study develops and validates neural network frameworks with physics-based constraints for surrogate modeling of rarefied gas dynamics across different levels of complexity. As a baseline, we first examine the BGK kinetic relaxation…

Mobile robots navigating in crowds trained using reinforcement learning are known to suffer performance degradation when faced with out-of-distribution scenarios. We propose that by properly accounting for the uncertainties of pedestrians,…

We introduce Roe Neural Networks (RoeNets) that can predict the discontinuity of the hyperbolic conservation laws (HCLs) based on short-term discontinuous and even continuous training data. Our methodology is inspired by Roe approximate…

Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a…

The propagation of traffic congestion along roads is a commonplace nonlinear phenomenon. When many roads are connected in a network, congestion can spill from one road to others as drivers queue to enter a congested road, creating further…

Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial differential equations (PDEs). This paper presents a rigorous…

Stability and safety are critical properties for successful deployment of automatic control systems. As a motivating example, consider autonomous mobile robot navigation in a complex environment. A control design that generalizes to…

Learning dynamical systems through purely data-driven methods is challenging as they do not learn the underlying conservation laws that enable them to correctly generalize. Existing port-Hamiltonian neural network methods have recently been…

This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable…

The solution of partial differential equations (PDEs) plays a central role in numerous applications in science and engineering, particularly those involving multiphase flow in porous media. Complex, nonlinear systems govern these problems…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

A one-dimensional driven lattice gas with disorder in the particle hopping probabilities is considered. It has previously been shown that in the version of the model with random sequential updating, a phase transition occurs from a low…

Modern urban resilience is threatened by cascading failures in multimodal transport networks, where localized shocks trigger widespread paralysis. Existing models, limited by their focus on pairwise interactions, often underestimate this…

Modern neural networks have shown promise for solving partial differential equations over surfaces, often by discretizing the surface as a mesh and learning with a mesh-aware graph neural network. However, graph neural networks suffer from…

Graph neural networks (GNNs) leverage message passing mechanisms to learn the topological features of graph data. Traditional GNNs learns node features in a spatial domain unrelated to the topology, which can hardly ensure topological…

In this thesis, we design algorithms for several NP-hard problems in both worst and beyond worst case settings. In the first part of the thesis, we apply the traditional worst case methodology and design approximation algorithms for the Hub…

Rigid body interactions are fundamental to numerous scientific disciplines, but remain challenging to simulate due to their abrupt nonlinear nature and sensitivity to complex, often unknown environmental factors. These challenges call for…

Learning to simulate complex physical systems from data has emerged as a promising way to overcome the limitations of traditional numerical solvers, which often require prohibitive computational costs for high-fidelity solutions. Recent…

Species transport models typically combine partial differential equations (PDEs) with relations from hindered transport theory to quantify electromigrative, convective, and diffusive transport through complex nanoporous systems; however,…

High-order Discontinuous Galerkin Spectral Element Methods (DGSEM) provide excellent accuracy for complex flow simulations, but their computational cost increases sharply with higher polynomial orders. %that provide very accurate solutions.…