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Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising…
Neural operator learning accelerates PDE solution by approximating operators as mappings between continuous function spaces. Yet in many engineering settings, varying geometry induces discrete structural changes, including topological…
We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic wave systems that are separated by straight interfaces. Such coupled simulations allow the application of the elastic…
Understanding shock-solid interactions remains a central challenge in compressiblefluiddynamics. WepresentJAX-Shock: afully-differentiable,GPU-accelerated, high-order shock-capturing solver for efficient simulation of the compressible…
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…
We propose a novel decomposition framework for the distributed optimization of Difference Convex (DC)-type nonseparable sum-utility functions subject to coupling convex constraints. A major contribution of the paper is to develop for the…
We propose derivative-informed neural operators (DINOs), a general family of neural networks to approximate operators as infinite-dimensional mappings from input function spaces to output function spaces or quantities of interest. After…
PDE-Constrained Optimization (PDECO) problems can be accelerated significantly by employing gradient-based methods with surrogate models like neural operators compared to traditional numerical solvers. However, this approach faces two key…
Federated learning must address heterogeneity, strict communication and computation limits, and privacy while ensuring performance. We propose an operator-theoretic framework that maps the $L^2$-optimal solution into a reproducing kernel…
Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the realization that access to the score -- the gradient of the…
Differential evolution (DE) is an effective global evolutionary optimization algorithm using to solve global optimization problems mainly in a continuous domain. In this field, researchers pay more attention to improving the capability of…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
The integration of optimization problems within neural network architectures represents a fundamental shift from traditional approaches to handling constraints in deep learning. While it is long known that neural networks can incorporate…
We present a neural operator framework for solving inverse scattering problems. A neural operator produces a preliminary indicator function for the scatterer, which, after appropriate rescaling, is used as a regularization parameter within…
In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…
Differential privacy (DP) offers a robust framework for safeguarding individual data privacy. To utilize DP in training modern machine learning models, differentially private optimizers have been widely used in recent years. A popular…
This paper proposes a differentiable robust LQR layer for reinforcement learning and imitation learning under model uncertainty and stochastic dynamics. The robust LQR layer can exploit the advantages of robust optimal control and…
We introduce the notion of discrete Baker-Akhiezer (DBA) modules, which are modules over the ring of difference operators, as a certain discretization of Baker-Akhiezer modules which are modules over the ring of differential operators. We…
We construct new, efficient, and accurate high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the…
Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is…