Related papers: Implicit Transfer Operator Learning: Multiple Time…
The current interpretation of stochastic gradient descent (SGD) as a stochastic process lacks generality in that its numerical scheme restricts continuous-time dynamics as well as the loss function and the distribution of gradient noise. We…
We present a neural-operator-accelerated concurrent multiscale framework that couples atomistic simulations with continuum finite-element analysis for history-dependent materials, thereby making atomistic-continuum multiscale simulations of…
Stochastic modeling of reaction networks is a framework used to describe the time evolution of many natural and artificial systems, including, biochemical reactive systems at the molecular level, viral kinetics, the spread of epidemic…
We propose an operator learning approach to accelerate geometric Markov chain Monte Carlo (MCMC) for solving infinite-dimensional Bayesian inverse problems (BIPs). While geometric MCMC employs high-quality proposals that adapt to posterior…
Neural networks are a commonly used approach to replace physical models with computationally cheap surrogates. Parametric uncertainty quantification can be included in training, assuming that an accurate prior distribution of the model…
Existing imitation learning works mainly assume that the demonstrator who collects demonstrations shares the same dynamics as the imitator. However, the assumption limits the usage of imitation learning, especially when collecting…
The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Ito stochastic calculus is obtained. The stochastic integral representation affords many…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
Learning PDE dynamics from limited data with unknown physics is challenging. Existing neural PDE solvers either require large datasets or rely on known physics (e.g., PDE residuals or handcrafted stencils), leading to limited applicability.…
Describing dynamics of a quantum system coupled to a complex many-body environment is a ubiquitous problem in quantum science. General non-Markovian environments are characterized by their influence matrix~(IM) -- a multi-time tensor…
Autoregressive surrogate models (or \textit{emulators}) of spatiotemporal systems provide an avenue for fast, approximate predictions, with broad applications across science and engineering. At inference time, however, these models are…
This paper proposes a real-time distributed operational architecture to efficiently coordinate intergrated transmission and distribution systems (ITD). At the distribution system level, the distribution system operator (DSO) computes the…
Self-supervised pretraining from static structures of drug-like compounds and proteins enable powerful learned feature representations. Learned features demonstrate state of the art performance on a range of predictive tasks including…
Quantum mechanics based ab-initio molecular dynamics (MD) simulation schemes offer an accurate and direct means to monitor the time-evolution of materials. Nevertheless, the expensive and repetitive energy and force computations required in…
Multi-scale simulations of nonlinear heterogeneous materials and composites are challenging due to the prohibitive computational costs of high-fidelity simulations. Recently, machine learning (ML) based approaches have emerged as promising…
This paper is concerned with networks of interacting linear systems at sites of a multidimensional lattice. The systems are governed by linear ODEs with constant coefficients driven by external inputs, and their internal dynamics and…
Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…
Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial differential equations over time. This work shows that…
Molecular dynamics simulations produce data with complex nonlinear dynamics. If the timestep behavior of such a dynamic system can be represented by a linear operator, future states can be inferred directly without expensive simulations.…