Related papers: Numerical Accuracy Matters: Applications of Machin…

Precision theoretical predictions for high multiplicity scattering rely on the evaluation of increasingly complicated scattering amplitudes which come with an extremely high CPU cost. For state-of-the-art processes this can cause technical…

We explore the influence of precision of the data and the algorithm for the simulation of chaotic dynamics by neural networks techniques. For this purpose, we simulate the Lorenz system with different precisions using three different neural…

Machine learning of multi-dimensional potential energy surfaces, from purely ab initio datasets, has seen substantial progress in the past years. Gaussian processes, a popular regression method, have been very successful at producing…

We introduce a local machine-learning method for predicting the electron densities of periodic systems. The framework is based on a numerical, atom-centred auxiliary basis, which enables an accurate expansion of the all-electron density in…

Neural fields have become widely used in various fields, from shape representation to neural rendering, and for solving partial differential equations (PDEs). With the advent of hybrid neural field representations like Instant NGP that…

Cutting edge deep learning techniques allow for image segmentation with great speed and accuracy. However, application to problems in materials science is often difficult since these complex models may have difficultly learning physical…

Neural network (NN) models are increasingly used in scientific simulations, AI, and other high performance computing (HPC) fields to extract knowledge from datasets. Each dataset requires tailored NN model architecture, but designing…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

Accurate simulation of atomic systems has the potential to revolutionize the design of molecules and materials. Unfortunately, exact solutions of the Schr\"odinger equation scale as O(N!) and remain inaccessible for systems with more than a…

Neural Networks (NNs) are effective models for refining the accuracy of molecular dynamics, opening up new fields of application. Typically trained bottom-up, atomistic NN potential models can reach first-principle accuracy, while…

We investigate how neural networks (NNs) understand physics using 1D quantum mechanics. After training an NN to accurately predict energy eigenvalues from potentials, we used it to confirm the NN's understanding of physics from four…

Enforcing universal symmetries in machine learning (ML) models is a common strategy to mitigate data scarcity. We show that exploiting exact, as well as approximate, label symmetries can benefit scaling laws. We illustrate the idea for the…

This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…

The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…

We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…

Motivated by recent research on Physics-Informed Neural Networks (PINNs), we make the first attempt to introduce the PINNs for numerical simulation of the elliptic Partial Differential Equations (PDEs) on 3D manifolds. PINNs are one of the…

Machine-learning-based interatomic potential energy surface (PES) models are revolutionizing the field of molecular modeling. However, although much faster than electronic structure schemes, these models suffer from costly computations via…

A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good…

The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…

Power consumption is a major obstacle in the deployment of deep neural networks (DNNs) on end devices. Existing approaches for reducing power consumption rely on quite general principles, including avoidance of multiplication operations and…