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Recent years have seen the development and growth of machine learning in high energy physics. There will be more effort to continue exploring its full potential. To make it easier for researchers to apply existing algorithms and neural…
Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in the fluid dynamics community,…
Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…
Energy-Based Models (EBMs) have proven to be a highly effective approach for modelling densities on finite-dimensional spaces. Their ability to incorporate domain-specific choices and constraints into the structure of the model through…
Nonlinear programming (NLP) plays a critical role in domains such as power energy systems, chemical engineering, communication networks, and financial engineering. However, solving large-scale, nonconvex NLP problems remains a significant…
In this paper we present a framework for solving two phase flow problems in porous media. The discretization is based on a Discontinuous Galerkin method and includes local grid adaptivity and local choice of polynomial degree. The method is…
This paper reports the development of a Python Non-Uniform Fast Fourier Transform (PyNUFFT) package, which accelerates non-Cartesian image reconstruction on heterogeneous platforms. Scientific computing with Python encompasses a mature and…
The Poisson-Boltzmann equation is widely used to model molecular electrostatics; however, it is usually solved in linearised form because the sinh nonlinearity is challenging, limiting its applicability in highly charged systems such as…
In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…
PySINDy is a Python package for the discovery of governing dynamical systems models from data. In particular, PySINDy provides tools for applying the sparse identification of nonlinear dynamics (SINDy) (Brunton et al. 2016) approach to…
Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the…
Rising computational demands of modern natural language processing (NLP) systems have increased the barrier to entry for cutting-edge research while posing serious environmental concerns. Yet, progress on model efficiency has been impeded…
Governments across the world are planning to increase the share of renewables in their energy systems. The siting of new wind and solar power plants requires close coordination with grid planning, and hence co-optimization of investment in…
The rapid advancement in AI architectures and the proliferation of AI-enabled systems have intensified the need for domain-specific architectures that enhance both the acceleration and energy efficiency of AI inference, particularly at the…
We present a novel technique for learning the mass matrices in samplers obtained from discretized dynamics that preserve some energy function. Existing adaptive samplers use Riemannian preconditioning techniques, where the mass matrices are…
In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming finite element methods to discretize the continuous…
Physics-informed neural networks (PINNs) in energy form, also known as the deep energy method (DEM), offer advantages over strong-form PINNs such as lower-order derivatives and fewer hyperparameters, yet dedicated and user-friendly software…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…
Solving large-scale nonlinear minimization problems is computationally demanding. Nonlinear multilevel minimization (NMM) methods explore the structure of the underlying minimization problem to solve such problems in a computationally…
Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and…