Related papers: RelaxNet: A structure-preserving neural network to…

Integrating machine learning techniques in established numerical solvers represents a modern approach to enhancing computational fluid dynamics simulations. Within the lattice Boltzmann method (LBM), the collision operator serves as an…

Modern approaches for simulation-based inference rely upon deep learning surrogates to enable approximate inference with computer simulators. In practice, the estimated posteriors' computational faithfulness is, however, rarely guaranteed.…

In this paper we present a new ultra efficient numerical method for solving kinetic equations. In this preliminary work, we present the scheme in the case of the BGK relaxation operator. The scheme, being based on a splitting technique…

In this work, we propose a uniformly accurate, structure-preserving neural surrogate for the radiative transfer equation with periodic boundary conditions based on a multiscale parity decomposition framework. The formulation introduces a…

This work is devoted to the analysis of the linear Boltzmann equation in a bounded domain, in the presence of a force deriving from a potential. The collision operator is allowed to be degenerate in the following two senses: (1) the…

We propose a novel \textit{capsule} based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet)…

Neural network based approximate computing is a universal architecture promising to gain tremendous energy-efficiency for many error resilient applications. To guarantee the approximation quality, existing works deploy two neural networks…

We introduce a multiplicative neural network architecture in which multiplicative interactions constitute the fundamental representation, rather than appearing as auxiliary components within an additive model. We establish a universal…

We present the Neural Satisfiability Network (NSNet), a general neural framework that models satisfiability problems as probabilistic inference and meanwhile exhibits proper explainability. Inspired by the Belief Propagation (BP), NSNet…

This paper proposes a novel neural network architecture inspired by the nonstandard form proposed by Beylkin, Coifman, and Rokhlin in [Communications on Pure and Applied Mathematics, 44(2), 141-183]. The nonstandard form is a highly…

Deep learning for predicting or generating 3D human pose sequences is an active research area. Previous work regresses either joint rotations or joint positions. The former strategy is prone to error accumulation along the kinematic chain,…

We introduce a structured approach to the construction of linear BGK-type collision operators ensuring that the resulting Lattice-Boltzmann methods are stable with respect to a weighted $L^2$-norm. The results hold for particular boundary…

In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to accurately and efficiently approximate functions with complex features, in terms of both degrees of freedom and computational cost. The…

In this paper, we put forward a neural network framework to solve the nonlinear hyperbolic systems. This framework, named relaxation neural networks(RelaxNN), is a simple and scalable extension of physics-informed neural networks(PINN). It…

Implicit neural networks, a.k.a., deep equilibrium networks, are a class of implicit-depth learning models where function evaluation is performed by solving a fixed point equation. They generalize classic feedforward models and are…

The Bhatnagar-Gross-Krook (BGK) single-relaxation-time collision model for the Boltzmann equation serves as the foundation of the lattice BGK (LBGK) method developed in recent years. The description of the collision as a uniform relaxation…

This article extends a recently introduced kinetic closure of turbulence by developing its theoretical framework, operational realizations, and validation. In contrast with filtered Navier--Stokes formulations, filtering the Boltzmann…

In recent years, various artificial intelligence-based surrogate models have been proposed to provide rapid manufacturability predictions of material forming processes. However, traditional AI-based surrogate models, typically built with…

Reinforcement Learning (RL) has demonstrated state-of-the-art results in a number of autonomous system applications, however many of the underlying algorithms rely on black-box predictions. This results in poor explainability of the…

Collision avoidance systems play a vital role in reducing the number of vehicle accidents and saving human lives. This paper extends the previous work using evolutionary neural networks for reactive collision avoidance. We are proposing a…