Related papers: EqOD: Symmetry-Informed Stability Selection for PD…

Temporal-Difference (TD) learning methods, such as Q-Learning, have proven effective at learning a policy to perform control tasks. One issue with methods like Q-Learning is that the value update introduces bias when predicting the TD…

In this work, we present a scalable Linear Matrix Inequality (LMI) based framework to verify the stability of a set of linear Partial Differential Equations (PDEs) in one spatial dimension coupled with a set of Ordinary Differential…

The focus of this paper is on stochastic variational inequalities (VI) under Markovian noise. A prominent application of our algorithmic developments is the stochastic policy evaluation problem in reinforcement learning. Prior…

Current semi-supervised object detection (SSOD) algorithms typically assume class balanced datasets (PASCAL VOC etc.) or slightly class imbalanced datasets (MS-COCO, etc). This assumption can be easily violated since real world datasets can…

Discovering the partial differential equations underlying spatio-temporal datasets from very limited and highly noisy observations is of paramount interest in many scientific fields. However, it remains an open question to know when model…

We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with…

When incorporating deep neural networks into robotic systems, a major challenge is the lack of uncertainty measures associated with their output predictions. Methods for uncertainty estimation in the output of deep object detectors (DNNs)…

Partial differential equations (PDEs) form a central component of scientific computing. Among recent advances in deep learning, evolutionary neural networks have been developed to successively capture the temporal dynamics of time-dependent…

Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by…

The superior performance of object detectors is often established under the condition that the test samples are in the same distribution as the training data. However, in many practical applications, out-of-distribution (OOD) instances are…

This paper aims to investigate the numerical approximation of semilinear non-autonomous stochastic partial differential equations (SPDEs) driven by multiplicative or additive noise. Such equations are more realistic than autonomous SPDEs…

Existing work in scientific machine learning (SciML) has shown that data-driven learning of solution operators can provide a fast approximate alternative to classical numerical partial differential equation (PDE) solvers. Of these, Neural…

In recent years, there has been a large increase in interest in numerical algorithms which preserve various qualitative features of the original continuous problem. Herein, we propose and investigate a numerical algorithm which preserves…

Recent work in data-driven modeling has demonstrated that a weak formulation of model equations enhances the noise robustness of a wide range of computational methods. In this paper, we demonstrate the power of the weak form to enhance the…

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…

Detecting and rejecting unknown out-of-distribution (OOD) samples is critical for deployed neural networks to void unreliable predictions. In real-world scenarios, however, the efficacy of existing OOD detection methods is often impeded by…

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

Out-of-distribution (OOD) detection is critical to ensure the safe deployment of deep learning models in critical applications. Deep learning models can often misidentify OOD samples as in-distribution (ID) samples. This vulnerability…

PDEs with periodic boundary conditions are frequently used to model processes in large spatial environments, assuming solutions to extend periodically beyond some bounded interval. However, solutions to these PDEs often do not converge to a…

Numerous methods have been proposed for global navigation satellite system (GNSS) receivers to detect faulty GNSS signals. One such fault detection and exclusion (FDE) method is based on the mathematical concept of Euclidean distance…