12 papers
When does least-squares residual minimization solve a differential equation?
Carlos Esteve-Yagüe, Richard Tsai, Stanley Osher
Least-squares residual minimization approximates a differential equation through an optimization problem. This paper investigates the conditions required to transition from station…
End-to-End Learning of Safe Optimal Feedback Control in High Dimensions with Control Barrier Function Layers
Xingjian Li, Kelvin Kan, Deepanshu Verma +3
We consider the problem of learning high-dimensional semi-global feedback controllers under hard safety constraints enforced by control barrier functions (CBFs). Incorporating CBFs…
Implicit Neural Optimal Transport via Fixed-Point Optimization
Yesom Park, Eric Gelphman, Stanley Osher +1
We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approache…
On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonians
Eric Gelphman, Deepanshu Verma, Nicole Tianjiao Yang +2
Optimal feedback control with implicit Hamiltonians poses a fundamental challenge for learning-based value function methods due to the absence of closed-form optimal control laws.…
End-to-End Training of High-Dimensional Optimal Control with Implicit Hamiltonians via Jacobian-Free Backpropagation
Eric Gelphman, Deepanshu Verma, Nicole Tianjiao Yang +2
Neural network approaches that parameterize value functions have succeeded in approximating high-dimensional optimal feedback controllers when the Hamiltonian admits explicit formu…
Neural Hamilton--Jacobi Characteristic Flows for Optimal Transport
Yesom Park, Shu Liu, Mo Zhou +1
We present a novel framework for solving optimal transport (OT) problems based on the Hamilton--Jacobi (HJ) equation, whose viscosity solution uniquely characterizes the OT map. By…
Thinking Out of the Box: Hybrid SAT Solving by Unconstrained Continuous Optimization
Zhiwei Zhang, Samy Wu Fung, Anastasios Kyrillidis +2
The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state…
Recent Advances in Numerical Solutions for Hamilton-Jacobi PDEs
Tingwei Meng, Siting Liu, Samy Wu Fung +1
Hamilton-Jacobi partial differential equations (HJ PDEs) play a central role in many applications such as economics, physics, and engineering. These equations describe the evolutio…
Solving Optimal Execution Problems via In-Context Operator Networks
Tingwei Meng, Moritz Voß, Nils Detering +3
We propose a novel transformer-based neural network architecture (ICON-OCnet) for solving optimal order execution problems in the presence of unknown price impact. Our architecture…
Fast Partial Fourier Transforms for Large-Scale Ptychography
Ricardo Parada, Samy Wu Fung, Stanley Osher
Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object i…
Laplace Meets Moreau: Smooth Approximation to Infimal Convolutions Using Laplace's Method
Ryan J. Tibshirani, Samy Wu Fung, Howard Heaton +1
We study approximations to the Moreau envelope -- and infimal convolutions more broadly -- based on Laplace's method, a classical tool in analysis which ties certain integrals to s…
Kernel Expansions for High-Dimensional Mean-Field Control with Non-local Interactions
Alexander Vidal, Samy Wu Fung, Stanley Osher +2
Mean-field control (MFC) problems aim to find the optimal policy to control massive populations of interacting agents. These problems are crucial in areas such as economics, physic…