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Development of comprehensive prediction models are often of great interest in many disciplines of science, but datasets with information on all desired features often have small sample sizes. We describe a transfer learning approach for…

Turbulence modeling remains a longstanding challenge in fluid dynamics. Recent advances in data-driven methods have led to a surge of novel approaches aimed at addressing this problem. This work builds upon our recent work [Phys. Rev.…

Restricted Boltzmann machines (RBMs) are a powerful class of generative models, but their training requires computing a gradient that, unlike supervised backpropagation on typical loss functions, is notoriously difficult even to…

Time-inhomogeneous finite-horizon Markov decision processes (MDP) are frequently employed to model decision-making in dynamic treatment regimes and other statistical reinforcement learning (RL) scenarios. These fields, especially healthcare…

We consider the commonly encountered situation (e.g., in weather forecasting) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous…

In this paper, we study the problem of transferring the available Markov Decision Process (MDP) models to learn and plan efficiently in an unknown but similar MDP. We refer to it as \textit{Model Transfer Reinforcement Learning (MTRL)}…

Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…

We introduce the Graded Transformer framework, a new class of sequence models that embeds algebraic inductive biases through grading transformations on vector spaces. Extending Graded Neural Networks (GNNs), we propose two architectures:…

The long-context capability of recent large transformer models can be surmised to rely on techniques such as attention/model parallelism, as well as hardware-level optimizations. While these strategies allow input lengths to scale to…

High-dimensional data in modern applications, such as COVID-19 mortality, often span multiple domains. Leveraging auxiliary information from source domains to improve performance in a target domain motivates the use of transfer learning.…

Climate models (CM) are used to evaluate the impact of climate change on the risk of floods and strong precipitation events. However, these numerical simulators have difficulties representing precipitation events accurately, mainly due to…

A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale…

In this paper, an $\mathscr{H}_2$ norm-based model reduction method for linear quantum systems is presented, which can obtain a physically realizable model with a reduced order for closely approximating the original system. The model…

In the pursuit of developing high-temperature alloys with improved properties for meeting the performance requirements of next-generation energy and aerospace demands, integrated computational materials engineering (ICME) has played a…

Guided by critical systems found in nature we develop a novel mechanism consisting of inhomogeneous polynomial regularisation via which we can induce scale invariance in deep learning systems. Technically, we map our deep learning (DL)…

Thermal radiative transfer (TRT) presents significant computational challenges due to the stiff, nonlinear coupling between radiation and material energy, particularly in multigroup, high-fidelity transport models. In this work, we develop…

Learning new tasks by drawing on prior experience gathered from other (related) tasks is a core property of any intelligent system. Gradient-based meta-learning, especially MAML and its variants, has emerged as a viable solution to…

Graph-based next-step prediction models have recently been very successful in modeling complex high-dimensional physical systems on irregular meshes. However, due to their short temporal attention span, these models suffer from error…

In turbulence modeling, we are concerned with finding closure models that represent the effect of the subgrid scales on the resolved scales. Recent approaches gravitate towards machine learning techniques to construct such models. However,…

Continual Learning (CL) aims to enable models to continuously acquire new knowledge from a sequence of tasks with avoiding the forgetting of learned information. However, existing CL methods only rely on the parameters of the most recent…