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Classifying the topology of closed curves is a central problem in low dimensional topology with applications beyond mathematics spanning protein folding, polymer physics and even magnetohydrodynamics. The central problem is how to determine…
Nuclear materials are often demanded to function for extended time in extreme environments, including high radiation fluxes and transmutation, high temperature and temperature gradients, stresses, and corrosive coolants. They also have a…
Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several…
Quantum many-body systems pose a formidable computational challenge due to the exponential growth of their Hilbert space. While machine learning (ML) has shown promise as an alternative paradigm, most applications remain at the…
Global climate models (GCMs) are the main tools for understanding and predicting climate change. However, due to limited numerical resolutions, these models suffer from major structural uncertainties; e.g., they cannot resolve critical…
Many real-world machine learning applications involve several learning tasks which are inter-related. For example, in healthcare domain, we need to learn a predictive model of a certain disease for many hospitals. The models for each…
We propose meta-curvature (MC), a framework to learn curvature information for better generalization and fast model adaptation. MC expands on the model-agnostic meta-learner (MAML) by learning to transform the gradients in the inner…
Improvements of Machine Learning (ML)-based radiation emulators remain constrained by the underlying assumptions to represent horizontal and vertical subgrid-scale cloud distributions, which continue to introduce substantial uncertainties.…
We derive a hierarchy of closures based on perturbations of well-known entropy-based closures; we therefore refer to them as perturbed entropy-based models. Our derivation reveals final equations containing an additional convective and…
First-principles computations are the driving force behind numerous discoveries of hydride-based superconductors, mostly at high pressures, during the last decade. Machine-learning (ML) approaches can further accelerate the future…
Meta-learning that uses implicit gradient have provided an exciting alternative to standard techniques which depend on the trajectory of the inner loop training. Implicit meta-learning (IML), however, require computing $2^{nd}$ order…
Machine learning-based closure models for LES have shown promise in capturing complex turbulence dynamics but often suffer from instabilities and physical inconsistencies. In this work, we develop a novel skew-symmetric neural architecture…
Continual learning aims to alleviate catastrophic forgetting when handling consecutive tasks under non-stationary distributions. Gradient-based meta-learning algorithms have shown the capability to implicitly solve the transfer-interference…
We introduce Spline Moment Equations (SME) for kinetic equations using a new weighted spline ansatz of the distribution function and investigate the ansatz, the model, and its performance by simulating the one-dimensional Boltzmann-BGK…
The $M_1$ minimum entropy moment system is a system of hyperbolic balance laws that approximates the radiation transport equation, and has many desirable properties. Among them are symmetric hyperbolicity, entropy decay, moment…
The application machine learning (ML) algorithms to turbulence modeling has shown promise over the last few years, but their application has been restricted to eddy viscosity based closure approaches. In this article we discuss rationale…
We present a novel algorithm for learning the parameters of hidden Markov models (HMMs) in a geometric setting where the observations take values in Riemannian manifolds. In particular, we elevate a recent second-order method of moments…
Multiscale problems can usually be approximated through numerical homogenization by an equation with some effective parameters that can capture the macroscopic behavior of the original system on the coarse grid to speed up the simulation.…
We study the closure problem for continuum balance equations that model mesoscale dynamics of large ODE systems. The underlying microscale model consists of classical Newton equations of particle dynamics. As a mesoscale model we use the…
In this paper, we develop a method for solving the problem of minimizing the $H^2$ error norm between the transfer functions of original and reduced systems on the set of stable matrices and two Euclidean spaces. That is, we develop a…