Related papers: Neural Network Matrix Product Operator: A Multi-Di…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

Deep Neural Networks (DNNs) require highly efficient matrix multiplication engines for complex computations. This paper presents a systolic array architecture incorporating novel exact and approximate processing elements (PEs), designed…

Accurately simulating systems governed by PDEs, such as voltage fields in cardiac electrophysiology (EP) modelling, remains a significant modelling challenge. Traditional numerical solvers are computationally expensive and sensitive to…

We investigate quantum-inspired tensor networks (QTNs) for approximating flow maps of hydrodynamic partial differential equations (PDEs). Motivated by the effective low-rank structure that emerges after tensorization of discretized…

Combining the excellent thermal and electrical properties of Cu with the high abrasion resistance and thermal stability of W, Cu-W nanoparticle-reinforced metal matrix composites and nano-multilayers (NMLs) are finding applications as…

The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this…

Machine learning potentials (MLPs) achieve near first-principles accuracy but often fail for atomic environments outside the training distribution. Active learning can mitigate this limitation; however, its application to large-scale…

Mathematical reasoning is a fundamental capability for large language models (LLMs), yet achieving high performance in this domain remains a significant challenge. The auto-regressive generation process often makes LLMs susceptible to…

Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. They involve physics beyond the reach of equilibrium statistical…

Neural Operators offer a powerful, data-driven tool for solving parametric PDEs as they can represent maps between infinite-dimensional function spaces. In this work, we employ physics-informed Neural Operators in the context of…

Automated hyperparameter optimization (HPO) can support practitioners to obtain peak performance in machine learning models. However, there is often a lack of valuable insights into the effects of different hyperparameters on the final…

Physics-informed neural networks (PINN) have been widely used in computational physics to solve partial differential equations (PDEs). In this study, we propose an energy-embedding-based physics-informed neural network method for solving…

We describe the development of machine-learned potentials of atmospheric gases with flexible monomers for molecular simulations. A recently suggested permutationally invariant polynomial neural network (PIP-NN) approach is utilized to…

Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural…

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…

Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. Nevertheless, there still exists a considerable accuracy gap between tensor network and the sophisticated…

Matrix product states (MPS) illustrate the suitability of tensor networks for the description of interacting many-body systems: ground states of gapped $1$-D systems are approximable by MPS as shown by Hastings [J. Stat. Mech. Theor. Exp.,…

Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…

We created a computational workflow to analyze the potential energy surface (PES) of materials using machine-learned interatomic potentials in conjunction with the minima hopping algorithm. We demonstrate this method by producing a…