Related papers: SymBoltz.jl: A symbolic-numeric, approximation-fre…
The Helmholtz equation is related to seismic exploration, sonar, antennas, and medical imaging applications. It is one of the most challenging problems to solve in terms of accuracy and convergence due to the scalability issues of the…
SYM-ILDL is a numerical software package that computes incomplete $LDL^{T}$ (or `ILDL') factorizations of symmetric indefinite and real skew-symmetric matrices. The core of the algorithm is a Crout variant of incomplete LU (ILU), originally…
This article presents numerical work on a special case of the cosmological semiclassical Einstein equation (SCE). The SCE describes the interaction of relativistic quantum matter by the expected value of the renormalized stress-energy…
SMLP: Symbolic Machine Learning Prover an open source tool for exploration and optimization of systems represented by machine learning models. SMLP uses symbolic reasoning for ML model exploration and optimization under verification and…
RelativisticDynamics.jl is an open-source Julia package for relativistic spin-orbital dynamics in the gravitational strong-field of a Kerr spacetime. Existing codes for modelling the dynamics of spinning objects like pulsars in the…
We present FreeBird, an extensible Julia-based platform for computational studies of phase equilibria at generic interfaces. The package supports a range of system configurations, from atomistic solid surfaces to coarse-grained…
Large Language Models (LLMs) have shown strong performance on code understanding tasks, yet they fundamentally lack the ability to perform precise, exhaustive mathematical reasoning about program behavior. Existing benchmarks either focus…
LLMs can solve program synthesis tasks but remain inefficient and unreliable on hard instances requiring large combinatorial search. Given a small set of reasoning traces, we use coding agents to compile them into reusable symbolic program…
The collisionless Boltzmann equation (CBE) is a fundamental equation that governs the dynamics of a broad range of astrophysical systems from space plasma to star clusters and galaxies. It is computationally expensive to integrate the CBE…
We define QSE, a symbolic execution framework for quantum programs by integrating symbolic variables into quantum states and the outcomes of quantum measurements. The soundness of QSE is established through a theorem that ensures the…
Integrating computational fluid dynamics (CFD) solvers into optimization and machine-learning frameworks is hampered by the rigidity of classic computational languages and the slow performance of more flexible high-level languages. In this…
We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can…
This research addresses the numerical simulation of the Boltzmann transport equation for semiconductor devices by proposing a multidimensional self-adaptive numerical simulation framework. This framework is applied to two important…
We present and discuss a framework for computer-aided multiscale analysis, which enables models at a "fine" (microscopic/stochastic) level of description to perform modeling tasks at a "coarse" (macroscopic, systems) level. These…
As the main theoretical support of quantum metrology, quantum parameter estimation must follow the steps of quantum metrology towards the applied science and industry. Hence, optimal scheme design will soon be a crucial and core task for…
We present the open source distributed software package Poisson-Boltzmann Analytical Method (PB-AM), a fully analytical solution to the linearized Poisson Boltzmann equation, for molecules represented as non-overlapping spherical cavities.…
This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…
State space models (SSMs) are a powerful and widely-used class of probabilistic models for analysing time-series data across various fields, from econometrics to robotics. Despite their prevalence, existing software frameworks for SSMs…
IFOSMONDI iterative algorithm for implicit co-simulation of coupled physical systems (introduced by the authors in july 2019 during the Simultech conference, p.176-186) enables us to solve the nonlinear coupling function while keeping the…
Traditional methods for solving physical equations in curved spaces, especially in fluid mechanics and general relativity, rely heavily on the use of Christoffel symbols. These symbols provide the necessary corrections to account for…