Related papers: Hybrid Symbolic-Numeric Framework for Power System…
This study extends the use of symbolic computation in Matrix Structural Analysis (MSA) to plane (2D) trusses, building on previous work that focused on continuous beams. An open-source MATLAB program, hosted on GitHub, was developed to…
The HPEC Graph Challenge is a collection of benchmarks representing complex workloads that test the hardware and software components of HPC systems, which traditional benchmarks, such as LINPACK, do not. The first benchmark, Subgraph…
A flexible and highly-extensible data assimilation testing suite, named DATeS, is described in this paper. DATeS aims to offer a unified testing environment that allows researchers to compare different data assimilation methodologies and…
In this paper we discuss three symbolic approaches for the generation of a finite difference scheme of a partial differential equation (PDE). We prove, that for a linear PDE with constant coefficients these three approaches are equivalent…
This article reviews recent progress in the development of the computing framework vector symbolic architectures (VSA) (also known as hyperdimensional computing). This framework is well suited for implementation in stochastic, emerging…
This article presents a new approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the…
Non-autonomous differential equations are crucial for modeling systems influenced by external signals, yet fitting these models to data becomes particularly challenging when the signals change abruptly. To address this problem, we propose a…
We consider the problem of symbolic-numeric integration of symbolic functions, focusing on rational functions. Using a hybrid method allows the stable yet efficient computation of symbolic antiderivatives while avoiding issues of…
In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…
In the steady-state contingency analysis, the traditional Newton-Raphson method suffers from non-convergence issues when solving post-outage power flow problems, which hinders the integrity and accuracy of security assessment. In this…
TeNeS (Tensor Network Solver) is a free/libre open-source software program package for calculating two-dimensional many-body quantum states based on the tensor network method and the corner transfer matrix renormalization group (CTMRG)…
We demonstrate a library for the integration of domain knowledge in deep learning architectures. Using this library, the structure of the data is expressed symbolically via graph declarations and the logical constraints over outputs or…
High-quality ordinary differential equation (ODE) solver libraries have a long history, going back to the 1970s. Over the past several years we have implemented, on top of the PETSc linear and nonlinear solver package, a new…
We present a general and automated approach for computing model gradients for PDE solvers built on sparse spectral methods, and implement this capability in the widely used open-source Dedalus framework. We apply reverse-mode automatic…
With the shift towards decentralized energy generation, the increasing complexity of power systems renders physics-based modeling challenging. At the same time the growing amount of available measurement data opens the door for obtaining…
Symbolic Regression (SR) enables the discovery of interpretable mathematical relationships from experimental and simulation data. These relationships are often coined descriptors which are defined as a fundamental materials property that is…
The design and analysis of systems that combine computational behaviour with physical processes' continuous dynamics - such as movement, velocity, and voltage - is a famous, challenging task. Several theoretical results from programming…
Computational X-ray absorption near-edge structure (XANES) is widely used to probe local coordination environments, oxidation states, and electronic structure in chemically complex systems. However, the use of computational XANES at scale…
Most numerical solvers and libraries nowadays are implemented to use mathematical models created with language-specific built-in data types (e.g. real in Fortran or double in C) and their respective elementary algebra implementations.…