Related papers: StablePDENet: Enhancing Stability of Operator Lear…
The field of adversarial robustness has attracted significant attention in machine learning. Contrary to the common approach of training models that are accurate in average case, it aims at training models that are accurate for worst case…
Neural operators have emerged as a powerful, discretization-invariant framework for solving partial differential equations (PDEs). Although established approaches like the Deep Operator Network (DeepONet) have successfully achieved…
Reinforcement learning is a general methodology of adaptive optimal control that has attracted much attention in various fields ranging from video game industry to robot manipulators. Despite its remarkable performance demonstrations, plain…
Decision-focused learning integrates predictive modeling and combinatorial optimization by training models to directly improve decision quality rather than prediction accuracy alone. Differentiating through combinatorial optimization…
In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization…
We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…
This paper proposes the Nerual Energy Descent (NED) via neural network evolution equations for a wide class of deep learning problems. We show that deep learning can be reformulated as the evolution of network parameters in an evolution…
Reinforcement learning (RL) has achieved remarkable success in a wide range of control and decision-making tasks. However, RL agents often exhibit unstable or degraded performance when deployed in environments subject to unexpected external…
Deep Neural Networks (DNNs) are becoming integral components of real world services relied upon by millions of users. Unfortunately, architects of these systems can find it difficult to ensure reliable performance as irrelevant details like…
Recently, the use of neural networks to accelerate the solving of partial differential equations (PDEs) has gained significant traction in both academia and industry. However, employing neural networks as standalone surrogate models raises…
We present a unified theoretical framework for analyzing the stability and consistency of Physics-Informed Neural Networks (PINNs), grounded in operator coercivity, variational formulations, and non-asymptotic perturbation theory. PINNs…
In adversarial machine learning, neural networks suffer from a significant issue known as robust overfitting, where the robust test accuracy decreases over epochs (Rice et al., 2020). Recent research conducted by Xing et al.,2021; Xiao et…
Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories;…
This paper addresses boundary prescribed-time stabilization of a one-dimensional heat equation with spatially and temporally varying coefficients. In contrast to asymptotic or exponential stabilization, prescribed-time stabilization ensures…
Deep neural networks (DNNs) are vulnerable to adversarial examples where inputs with imperceptible perturbations mislead DNNs to incorrect results. Despite the potential risk they bring, adversarial examples are also valuable for providing…
Minimizing PDE-residual losses is a common strategy to promote physical consistency in neural operators. However, standard formulations often lack variational correctness, meaning that small residuals do not guarantee small solution errors…
Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers…
We develop a novel framework for uncertainty quantification in operator learning, the Stochastic Operator Network (SON). SON combines the stochastic optimal control concepts of the Stochastic Neural Network (SNN) with the DeepONet. By…
Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…
We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…