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Finding the maximum cut of a graph (MAXCUT) is a classic optimization problem that has motivated parallel algorithm development. While approximate algorithms to MAXCUT offer attractive theoretical guarantees and demonstrate compelling…
We present a neural network-based method for learning scalar hyperbolic conservation laws. Our method replaces the traditional numerical flux in finite volume schemes with a trainable neural network while preserving the conservative…
We consider a Brownian particle diffusing in a one dimensional interval with absorbing end points. We study the ramifications when such motion is interrupted and restarted from the same initial configuration. We provide a comprehensive…
We consider the non-equilibrium dynamics of disordered systems as defined by a master equation involving transition rates between configurations (detailed balance is not assumed). To compute the important dynamical time scales in…
End-to-end performance estimation and measurement of deep neural network (DNN) systems become more important with increasing complexity of DNN systems consisting of hardware and software components. The methodology proposed in this paper…
As neural interfaces become more advanced, there has been an increase in the volume and complexity of neural data recordings. These interfaces capture rich information about neural dynamics that call for efficient, real-time processing…
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second…
Machine learning models have become indispensable tools in applications across the physical sciences. Their training is often time-consuming, vastly exceeding the inference timescales. Several protocols have been developed to perturb the…
Machine learning (ML) entered the field of computational micromagnetics only recently. The main objective of these new approaches is the automatization of solutions of parameter-dependent problems in micromagnetism such as fast response…
The prohibitive cost and low fidelity of experimental data in industry scale thermofluid systems limit the usefulness of pure data-driven machine learning methods. Physics-informed neural networks (PINN) strive to overcome this by embedding…
The $L^2$ gradient flow of the Ginzburg-Landau free energy functional leads to the Allen Cahn equation that is widely used for modeling phase separation. Machine learning methods for solving the Allen-Cahn equation in its strong form suffer…
Spiking neural networks (SNNs) represent a promising approach in machine learning, combining the hierarchical learning capabilities of deep neural networks with the energy efficiency of spike-based computations. Traditional end-to-end…
Neuromorphic computing is henceforth a major research field for both academic and industrial actors. As opposed to Von Neumann machines, brain-inspired processors aim at bringing closer the memory and the computational elements to…
We present a partitioned neural network-based framework for learning of fluid-structure interaction (FSI) problems. We decompose the simulation domain into two smaller sub-domains, i.e., fluid and solid domains, and incorporate an…
In this paper, we investigate neural networks applied to multiscale simulations and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Due to the multiscale nature of the medium, the fine-grid…
The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study…
Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some…
In this paper we present a comprehensive analysis of the solution of the classical problem of finding the distribution density of a random variable - the first passage time to a given domain by the trajectory of a $p$-adic Markov stochastic…
Physics-informed neural networks (PINNs) show great advantages in solving partial differential equations. In this paper, we for the first time propose to study conformable time fractional diffusion equations by using PINNs. By solving the…
Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…