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Learning data representations under uncertainty is an important task that emerges in numerous scientific computing and data analysis applications. However, uncertainty quantification techniques are computationally intensive and become…

Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic…

Materials exhibiting a substitutional disorder such as multicomponent alloys and mixed metal oxides/oxyfluorides are of great importance in many scientific and technological sectors. Disordered materials constitute an overwhelmingly large…

Using the maximum entropy method, we derive the "adaptive cluster expansion" (ACE), which can be trained to estimate probability density functions in high dimensional spaces. The main advantage of ACE over other Bayesian networks is its…

A number of methods have been proposed for causal effect estimation, yet few have demonstrated efficacy in handling data with complex structures, such as images. To fill this gap, we propose Causal Multi-task Deep Ensemble (CMDE), a novel…

Spectral clustering is a popular method for effectively clustering nonlinearly separable data. However, computational limitations, memory requirements, and the inability to perform incremental learning challenge its widespread application.…

Since the introduction of deep learning for solving partial differential equations (PDEs), there has been growing interest in real-time system responses, where the kernel function plays a key role. Physics-informed neural networks (PINNs),…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

Ordinary differential equations (ODEs) are a conventional way to describe the observed dynamics of physical systems. Scientists typically hypothesize about dynamical behavior, propose a mathematical model, and compare its predictions to…

Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

Probabilistic programming languages (PPLs) are an expressive means of representing and reasoning about probabilistic models. The computational challenge of probabilistic inference remains the primary roadblock for applying PPLs in practice.…

This paper solves a new class of optimization problems under uncertainty, called Probable Event Constrained Optimization (PECO), which optimizes an objective function of decision variables and subjects to a set of Probable Event Constraints…

Multivariate imputation by chained equations (MICE) is one of the most popular approaches to address missing values in a data set. This approach requires specifying a univariate imputation model for every variable under imputation. The…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods…

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

Deep neural networks has been increasingly applied in fault diagnostics, where it uses historical data to capture systems behavior, bypassing the need for high-fidelity physical models. However, despite their competence in prediction tasks,…

In recent years we have witnessed a growing interest in various non-equilibrium systems described in terms of stochastic non-linear field theories. In some of those systems like the KPZ and related models, the interesting behavior is in the…