Related papers: Polyconvex neural network models of thermoelastici…

We study the feasibility of data based machine learning applied to ultrasound tomography to estimate water-saturated porous material parameters. In this work, the data to train the neural networks is simulated by solving wave propagation in…

We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing…

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…

Deep learning is having a tremendous impact in many areas of computer science and engineering. Motivated by this success, deep neural networks are attracting an increasing attention in many other disciplines, including physical sciences. In…

Compressing neural nets is an active research problem, given the large size of state-of-the-art nets for tasks such as object recognition, and the computational limits imposed by mobile devices. We give a general formulation of model…

Anisotropy in the mechanical response of materials with microstructure is common and yet is difficult to assess and model. To construct accurate response models given only stress-strain data, we employ classical representation theory, novel…

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…

In many real-world deployments of machine learning systems, data arrive piecemeal. These learning scenarios may be passive, where data arrive incrementally due to structural properties of the problem (e.g., daily financial data) or active,…

The aim of this paper is to develop a general framework for training neural networks (NNs) in a distributed environment, where training data is partitioned over a set of agents that communicate with each other through a sparse, possibly…

This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…

Accurate thermal analysis of composites and porous media requires detailed characterization of local thermal properties in small scale. For some important applications such as lithium-ion batteries, changes in the properties during the…

Tensor networks are a very powerful data structure tool originating from quantum system simulations. In recent years, they have seen increased use in machine learning, mostly in trainings with gradient-based techniques, due to their…

Hyperparameters and learning algorithms for neuromorphic hardware are usually chosen by hand. In contrast, the hyperparameters and learning algorithms of networks of neurons in the brain, which they aim to emulate, have been optimized…

Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation…

In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…

Effectively representing heterogeneous tabular datasets for meta-learning purposes remains an open problem. Previous approaches rely on predefined meta-features, for example, statistical measures or landmarkers. The emergence of dataset…

We provide a mathematical interpretation of convolutional (or message passing) neural networks by using presheaves and copresheaves of the set of continuous functions over a topological space. Based on this interpretation, we formulate a…

Neural networks are a promising technique for parameterizing sub-grid-scale physics (e.g. moist atmospheric convection) in coarse-resolution climate models, but their lack of interpretability and reliability prevents widespread adoption.…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

Coupling of physics across length and time scales plays an important role in the response of microstructured materials to external loads. In a multi-scale framework, unresolved (subgrid) meso-scale dynamics is upscaled to the homogenized…