Related papers: StablePDENet: Enhancing Stability of Operator Lear…

A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models…

Recent advancements in artificial intelligence, particularly deep neural networks, have pushed the boundaries of what is achievable in complex tasks. Traditional methods for training neural networks in classification problems often rely on…

Despite the high performance achieved by deep neural networks on various tasks, extensive studies have demonstrated that small tweaks in the input could fail the model predictions. This issue of deep neural networks has led to a number of…

When learning behavior, training data is often generated by the learner itself; this can result in unstable training dynamics, and this problem has particularly important applications in safety-sensitive real-world control tasks such as…

Ensuring solution feasibility is a key challenge in developing Deep Neural Network (DNN) schemes for solving constrained optimization problems, due to inherent DNN prediction errors. In this paper, we propose a ``preventive learning''…

Despite their impressive performance, contemporary neural networks often lack structural safeguards that promote stable learning and interpretable behavior. In this work, we introduce a reformulation of layer-level transformations that…

We develop a data-driven machine learning approach to identifying parameters with steady-state solutions, locating such solutions, and determining their linear stability for systems of ordinary differential equations and dynamical systems…

This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating…

We study the model robustness against adversarial examples, referred to as small perturbed input data that may however fool many state-of-the-art deep learning models. Unlike previous research, we establish a novel theory addressing the…

Deep neural networks have proven remarkably effective at solving many classification problems, but have been criticized recently for two major weaknesses: the reasons behind their predictions are uninterpretable, and the predictions…

A kernel-based approach for the learning of the solution operator of general nonhomogeneous partial differential equations (PDEs) is proposed. The method incorporates physical priors, typically encoded through the PDE operator, into a…

When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…

This paper investigates the mean square exponential stabilization problem for a class of coupled PDE-ODE systems with Markov jump parameters. The considered system consists of multiple coupled hyperbolic PDEs and a finite-dimensional ODE,…

An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…

This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…

Neural Ordinary Differential Equations (NODEs) probed the usage of numerical solvers to solve the differential equation characterized by a Neural Network (NN), therefore initiating a new paradigm of deep learning models with infinite depth.…

In this work, we describe a novel approach to building a neural PDE solver leveraging recent advances in transformer based neural network architectures. Our model can provide solutions for different values of PDE parameters without any need…

Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well…

Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly…

This paper proposes an attack-independent (non-adversarial training) technique for improving adversarial robustness of neural network models, with minimal loss of standard accuracy. We suggest creating a neighborhood around each training…