Related papers: Designing Neural Networks for Hyperbolic Conservat…

This work presents a new approach for premixed turbulent combustion modeling based on convolutional neural networks (CNN). We first propose a framework to reformulate the problem of subgrid flame surface density estimation as a machine…

Two models based on convolutional neural networks are trained to predict the two-dimensional velocity-fluctuation fields at different wall-normal locations in a turbulent open channel flow, using the wall-shear-stress components and the…

In the present study, the capabilities of a new Convolutional Neural Network (CNN) model are explored with the paramount objective of reconstructing the temperature field of wall-bounded flows based on a limited set of measurement points…

Generative Flow Networks (GFlowNets; GFNs) are a class of generative models that learn to sample compositional objects proportionally to their a priori unknown value, their reward. We focus on the case where the reward has a specified,…

Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a…

Control Barrier Functions (CBF) have been recently utilized in the design of provably safe feedback control laws for nonlinear systems. These feedback control methods typically compute the next control input by solving an online Quadratic…

Physics-informed neural networks have been widely applied to partial differential equations with great success because the physics-informed loss essentially requires no observations or discretization. However, it is difficult to optimize…

Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often…

Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should…

Deep neural network models have shown a great potential in accelerating the simulation of fluid dynamic systems. Once trained, these models can make inference within seconds, thus can be extremely efficient. However, they suffer from a…

We propose the physics-constrained convolutional neural network (PC-CNN) to infer the high-resolution solution from sparse observations of spatiotemporal and nonlinear partial differential equations. Results are shown for a chaotic and…

We develop a representation suitable for the unconstrained recognition of words in natural images: the general case of no fixed lexicon and unknown length. To this end we propose a convolutional neural network (CNN) based architecture which…

In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this…

Deep Neural Networks (DNNs) deliver impressive performance but their black-box nature limits deployment in high-stakes domains requiring transparency. We introduce Compositional Function Networks (CFNs), a novel framework that builds…

Graph neural networks (GNNs) have emerged as a versatile and efficient option for modeling the dynamic behavior of deformable materials. While GNNs generalize readily to arbitrary shapes, mesh topologies, and material parameters, existing…

Deep Learning methods have seen a wide range of successful applications across different industries. Up until now, applications to physical simulations such as CFD (Computational Fluid Dynamics), have been limited to simple test-cases of…

We study the applicability of a Deep Neural Network (DNN) approach to simulate one-dimensional non-relativistic fluid dynamics. Numerical fluid dynamical calculations are used to generate training data-sets corresponding to a broad range of…

Recurrent neural networks are capable of learning the dynamics of an unknown nonlinear system purely from input-output measurements. However, the resulting models do not provide any stability guarantees on the input-output mapping. In this…

Turbulence plays an important role in astrophysical phenomena, including core-collapse supernovae (CCSN), but current simulations must rely on subgrid models since direct numerical simulation (DNS) is too expensive. Unfortunately, existing…

We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent…