Related papers: Stability of implicit neural networks for long-ter…

Power distribution networks are approaching their voltage stability boundaries due to the severe voltage violations and the inadequate reactive power reserves caused by the increasing renewable generations and dynamic loads. In the broad…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

In recent years, nonlinear dynamic system identification using artificial neural networks has garnered attention due to its broad potential applications across science and engineering. However, purely data-driven approaches often struggle…

Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many…

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 modern transportation systems, an enormous amount of traffic data is generated every day. This has led to rapid progress in short-term traffic prediction (STTP), in which deep learning methods have recently been applied. In traffic…

This work investigates the detection of instabilities that may occur when utilizing deep learning models for image reconstruction tasks. Although neural networks often empirically outperform traditional reconstruction methods, their usage…

Review of implicit methods of integrating system of stiff ordinary differential equations is presented. Defines and graphically presents absolute stability region for Gears methods (backward differentiation formula) used to solve system of…

This work establishes a rigorous connection between stability properties of discrete-time algorithms (DTAs) and corresponding continuous-time dynamical systems derived through $ O(s^r) $-resolution ordinary differential equations (ODEs). We…

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by…

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…

Many important problems in the real world don't have unique solutions. It is thus important for machine learning models to be capable of proposing different plausible solutions with meaningful probability measures. In this work we introduce…

A fundamental challenge in car-following modeling lies in accurately representing the multi-scale complexity of driving behaviors, particularly the intra-driver heterogeneity where a single driver's actions fluctuate dynamically under…

Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…

Learned optimizers -- neural networks that are trained to act as optimizers -- have the potential to dramatically accelerate training of machine learning models. However, even when meta-trained across thousands of tasks at huge…

Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over…

Temporal difference (TD) learning is a foundational algorithm in reinforcement learning (RL). For nearly forty years, TD learning has served as a workhorse for applied RL as well as a building block for more complex and specialized…

We discover restrained numerical instabilities in current training practices of deep networks with stochastic gradient descent (SGD), and its variants. We show numerical error (on the order of the smallest floating point bit and thus the…

We consider a deep structured linear network under sparsity constraints. We study sharp conditions guaranteeing the stability of the optimal parameters defining the network. More precisely, we provide sharp conditions on the network…

Recent advances in deep learning have led to a paradigm shift in the field of reversible steganography. A fundamental pillar of reversible steganography is predictive modelling which can be realised via deep neural networks. However,…