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Extracting automatically the complex set of features composing real high-dimensional data is crucial for achieving high performance in machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically known to be efficient for…

High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…

Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…

'Data' plays a central role in data-driven methods, but is not often the subject of focus in investigations of machine learning algorithms as applied to Earth System Modeling related problems. Here we consider the case of eddy-mean…

Turbulence simulation with classical numerical solvers requires high-resolution grids to accurately resolve dynamics. Here we train learned simulators at low spatial and temporal resolutions to capture turbulent dynamics generated at high…

Computational fluid dynamics models based on Reynolds-averaged Navier--Stokes equations with turbulence closures still play important roles in engineering design and analysis. However, the development of turbulence models has been stagnant…

We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment…

Data-driven turbulence modelling approaches are gaining increasing interest from the CFD community. However, the introduction of a machine learning (ML) model introduces a new source of uncertainty, the ML model itself. Quantification of…

Ionic models, described by systems of stiff ordinary differential equations, are fundamental tools for simulating the complex dynamics of excitable cells in both Computational Neuroscience and Cardiology. Approximating these models using…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

Fluid turbulence is an important problem for physics and engineering. Turbulence modeling deals with the development of simplified models that can act as surrogates for representing the effects of turbulence on flow evolution. Such models…

We study the random processes with non-local memory and obtain new solutions of the Mori-Zwanzig equation describing non-markovian systems. We analyze the system dynamics depending on the amplitudes $\nu$ and $\mu_0$ of the local and…

Stochastic and soft optimal policies resulting from entropy-regularized Markov decision processes (ER-MDP) are desirable for exploration and imitation learning applications. Motivated by the fact that such policies are sensitive with…

The idea of decision-aware model learning, that models should be accurate where it matters for decision-making, has gained prominence in model-based reinforcement learning. While promising theoretical results have been established, the…

Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…

Data-driven turbulence modeling studies have reached such a stage that the fundamental framework is basically settled, but several essential issues remain that strongly affect the performance, including accuracy, smoothness, and…

Many physical systems are described by probability distributions that evolve in both time and space. Modeling these systems is often challenging to due large state space and analytically intractable or computationally expensive dynamics. To…

We study the performance of long short-term memory networks (LSTMs) and neural ordinary differential equations (NODEs) in learning latent-space representations of dynamical equations for an advection-dominated problem given by the viscous…

Unraveling the structural factors influencing the dynamics of amorphous solids is crucial. While deep learning aids in navigating these complexities, transparency issues persist. Inspired by the successful application of prototype neural…

Markov chain Monte Carlo (MCMC) is a key algorithm in computational statistics, and as datasets grow larger and models grow more complex, many popular MCMC algorithms become too computationally expensive to be practical. Recent progress has…