Mathematical Software
Roughly includes material in ACM Subject Class G.4.
sort pith recommended most recent
Euler-Poisson test passes convergence, Jeans-instability, and Sedov blast-wave checks.
· “Multi-Solver Coupling for Parallel Adaptive Multi-Physics Simulations with Trixi.jl and deal.II”
Kokkos code matches specialized single-GPU speed while enabling billion-particle spectral plasma runs on three supercomputers
· “A Performance-Portable, Massively Parallel Distributed Nonuniform FFT”
Fine-tuned models inside a feedback loop outperform larger general models on verified FEniCS scripts for solids, fluids, and multiphysics.
· “ALL-FEM: Agentic Large Language models Fine-tuned for Finite Element Methods”
A modular framework computes the adjoint automatically, so variational and ensemble methods can share one differentiable codebase.
Sampling Weyl characters at rational points yields every multiplicity, with explicit tensor contractions and proof-certified output.
· “Decomposing Grassmann Monomials for Superfield Expansions”
Open-source package for graded superspace expressions outruns established systems on tested operations.
· “Alakazam: Symbolic Tensor Algebra for Field Theory in Julia”
Physics stays in C/C++; the compiler fuses both worlds in MLIR and replaces hundreds of handwritten lines with tens.
· “DSLHyPE-a DSL kernel language for the Exascale Hyperbolic PDE Engine ExaHyPE”
Reports record the build, toolchain, flags, and run settings, so numbers can be trusted and rerun.
· “Performance Reporting of Mathematical Library Installations with LAAB - An Overview”
On the Taylor-Green vortex at Mach 1.25 it matches reference dilatational dissipation 30% better than the next solver.
· “Lattice Boltzmann Method for Compressible Navier-Stokes-Fourier Equations”
No factorizations: restarted averaged PDHG shrinks error geometrically and scales to 440 million variables.
An open-source JAX library trains compact CP and tensor-train models to competitive RMSE on three benchmarks.
A new tool maps step-bounded reachability to dense tensor code and reports up to 300x speedups on dense benchmarks.
· “Tensor Probabilistic Model Checking of Finite-Horizon Markov Chains (Extended Version)”
Aligned settings and even single-package retuning both swing wall time by orders of magnitude
· “Performance Benchmarking: Software for the Density Matrix Renormalization Group”
Correctly rounded arbitrary precision was missing on GPUs; this port delivers it with verified bit-for-bit results.
Swap between projection-based ROMs and data-only surrogates, and chain them, without changing solver wrappers.
Benchmark across Rust, Java, Go, TypeScript, C++, Julia shows erasure and boxing, not abstraction, create the slowdowns.
· “Progress in Benchmarking Generics for Mathematical Computation”
A high-level dynamic language can stand in for Fortran in large MPI runs.
A web TQFT tool builds the diagrams, computes colored invariants, and names the knots
· “A TQFT-based Platform for Efficient Computation of Knot Invariants”
A JAX-native solver turns index-reduced multi-physics models into differentiable primitives for inversion, control, and design.
No tables, no power series: contractive fixed points yield the functions and fast vector code.
· “A Fixed-Point Construction of the Elementary Transcendental Functions”
A GPU simulator reproduces XXX-model autocorrelation on a 68-site processor graph at ~10x the speed of the reference.
· “Tensor Network Simulation of the Heisenberg Model on Heavy-Hex Lattices”
autotn groups shared prefixes and suffixes into virtual states, then checks small networks against dense references.
· “autotn: Automata-inspired construction of tensor-network operators from symbolic local rules”
A mean-square formula ranks summation trees by predicted error and fixes optimal block sizes, validated across four precisions.
· “A Second-Moment Theory for Floating-Point Reduction Trees”
Monotone design problems compose via series, parallel, and feedback; Kleene iteration finds the minimal resources.
· “texttt{codesign-mcdp}: A Python Library for Monotone Co-Design Problems”
A Python library reaches 10⁻⁹ residuals and recovers a 90-degree rotation to within 0.07 degrees on four planar tests.
· “anyakrakusuma: A Python Library for Entropic Schr\"odinger Bridges on Idealized Geometries”
A drop-in library speeds training 2.3x and kernels 19x, with gradients matching finite-difference references.
· “FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solvers”
Open-source tool computes full stable and unstable response branches from equations alone—no hand-derived Jacobians.
A single layer reports only justifiable duals and sensitivities, and runs what-if batches near bare-solver cost.
· “pyoptexplain: A Python Library for Post-Optimality Analysis and Explanation of Optimization Models”
Experiment with custom OCP MX formats and undocumented GPU settings without hardware
· “Simulation of Custom-Precision OCP MX Block Floating-Point Formats and Arithmetic”
First public database of the Gukov–Manolescu invariant from Park’s inverted state sum
Symbolic group functions in a Gelfand–Tsetlin basis, without building the full matrix
Unanchored Lie-exponential search recovers exact triples and a hub-triangle, then fully defective configs for n=5,6
AcadGIS scripts boundaries, locators, layers, and PNG/PDF/SVG export for paper-ready figures.
· “AcadGIS: A Single-Import Python Package for Reproducible, Publication-Ready Academic Maps”
Open Planner-Worker-Verifier loop raises success under a fixed token budget and stays human-steerable.
· “OpenProver: Agentic and Interactive Theorem Proving with Lean 4”
Four variants keep local convergence; removing the sync barrier cuts wall-clock time most
· “Parallel versions of the mesh adaptive direct search algorithm”
JAX-FVM combines entropy-stable finite-volume numerics with end-to-end automatic differentiation on triangular grids, enabling gradientbased
By splitting doubles into padded 13-bit pieces, matrix products gain double-double accuracy at 13.75 TFLOPS on A100 — faster than regular FP
IID methods fall to 28% on AR(1); a unified library couples resampling with adaptive conformal intervals
· “tsbootstrap: Distribution-Free Uncertainty Quantification and Conformal Prediction for Time Series”
Declare the PDE; get a second-order GPU kernel that hits 96% of memory bandwidth.
· “Automated Derivation of Lattice Boltzmann Methods for Systems of Conservation Laws”
A quickselect-style partition replaces the usual n-log-n sort for discrete risk measures
Open branch-and-cut study shows comb, fixing and SPI add nothing on 76 instances
Subtraction-free GTH kernels on triplet data beat standard solvers on tiny entries
· “The mmatrix toolbox: componentwise accurate algorithms for M-matrices with triplet representation”
The unitary factor preserves the original solution set for zero- and positive-dimensional cases, extending numerical methods beyond linear a
Zero-malloc workspace and device-only permutations remove host bottlenecks during Heisenberg-picture contraction.
· “GPU-First Heisenberg-Picture Tensor Network Dynamics for the 2D Transverse-Field Ising Model”
bgspprc uses compile-time resources and bucket-graph labelling for faster pricing in vehicle routing solvers.
New formula from CRT uniqueness condition guarantees validity for any input scaling at no extra cost and matches accurate-mode accuracy at f
Users set monotonicity, positivity and other rules; coefficients are written to plain text usable in any code.
· “pyDOF: a Python library for the design of discrete forward and inverse filters”
By keeping Ozaki intermediates on-chip, EmuGEMM beats cuBLAS TF32 by up to 1.7x on Hopper and Blackwell at matching accuracy.
· “EmuGEMM: Fused Tensor Core Kernels for Precision Emulation in Matrix Multiplication”
Machine-checked proofs cover Armijo, Wolfe conditions and global convergence for gradient-based methods
Mining each kernel's own error distribution lifts bug recall from 73.2% to 82.4% with 20 new false positives.
· “Operator-Aware Mixed-Precision Tolerance Calibration for Tensor Kernels”
Explicit degree-aware bounds from Dyson-Duhamel expansion give finite-degree estimates and improve on prior results for test ODEs.
Access-pattern decomposition of particle data lowers total offloading overhead by 12-25% as transfers dominate runtime.
Previous techniques either miss the points or use non-arc-length parameterization; this keeps both.
Local clocks and static buffers advance only active sub-graphs while eliminating dynamic memory allocation and interpolation.
· “An Asynchronous multi-rate Taylor method for Delay Differential Equations”
High-level abstractions for spectral/hp operators lower progressively with domain optimizations at each stage.
Register storage of unevaluated 64-bit sums supports GPU tasking for higher precision without custom libraries.
Non-nested global space enables communication-free interpolation inside two-level Schwarz method for pMG pressure Poisson solves
· “Coarse Solvers for Exascale Solution of Poisson Problems”
MaRDI Open Interfaces standardizes connections to different solvers, freeing researchers to focus on experiments like PINN training for PDEs
· “Software package MaRDI Open Interfaces for improved interoperability in numerical optimization”
Automated marshalling cuts code changes when testing multiple solvers across languages.
· “MaRDI Open Interfaces for Interoperable Nonlinear Optimization”
Benchmarks across SpMV, Lanczos, and exponential workloads show native Rust code tracks state-of-the-art CSC performance.
· “Evaluating Rust for Sparse Matrix Kernels in Scientific Computing”
By learning latent representations and propensity scores together, the method matches units to recover counterfactuals under hidden bias and
· “Balanced Twins: Causal Inference on Time Series with Hidden Confounding”
Suite of structural checks on five benchmarks shows single error score misses coherence failures
· “A Diagnostic Software Suite for Auditing Learned PDE Simulators”
Store numbers as numerator/denominator pairs, divide once at the end, deep gradients stay exact within 2^53.
A node-by-node trace shows why create_graph=True is essential for physics-informed training.
Compiles lazy tensor graphs to native ANE programs that finish ResNet-18 forward passes in 0.33 ms and support training.
· “ANEForge: Python for direct computation on the Apple Neural Engine”
Ill-conditioned PDE systems that defeat plain Krylov solvers can sit inside gradient-based optimization loops.
· “JAX-AMG: A GPU-Accelerated Differentiable Sparse Linear Solver Library for JAX”
Dynamic and steady-state Python versions match published references and give consistent MLSS estimates.
A systematic search plus validation produces mixed-precision variants that meet accuracy targets while cutting memory and energy use in nume
CATEKAPPA lets users without programming skills design consistency tests and interpret categorical agreement via a web app.
Integer-only Newton method fills the large-precision gap left by existing CUDA libraries.
· “On GPU Implementation for Multi-Precision Integer Division”
Active enumeration on Vietoris-Rips filtrations cuts time and memory versus standard algorithms.
· “RedZeD: Computing persistent homology by Reduction to Zero Differentials”
Microbenchmarks on AArch64 and x86-64 show local bit operations beat heap reads for tags while NaN-boxing saves allocation for floats.
Upper and lower envelopes on scattered points produce continuous approximations that obey ordering rules and run on graphics hardware.
· “Fitting scattered data with optional monotonicity constraints on GPU: LipFit package”
Ozaki-Bailey projects 18 ms for 1024 cubed at full precision versus 12.9 ms memory roof
Replaces method-of-moments approximations in Baum-Welch with ECME and Newton-Raphson for Gamma, Beta, Weibull and others.
· “libhmm: A Modern C++20 Library for Hidden Markov Models with Correct MLE Emission M-Steps”
Wasserstein rates recover near 0.5 while strong L1 error collapses in extreme compressible turbulence
· “Computing statistical solutions of a Mach 2000 astrophysical jet”
Handles Weingarten calculus for unitary, orthogonal, symplectic and other groups with symbolic dimension support.
· “IntegrateUnitary.jl: A Julia package for symbolic integration over Haar measures”
Ehrhart-Macdonald reciprocity turns many negative evaluations into quick or zero strict-pattern counts, and adaptive choice yields practical
· “Fast computation of Ehrhart polynomials of Gelfand--Tsetlin polytopes via Macdonald reciprocity”
Distortion method hides matrix data from untrusted servers yet returns the exact original determinant after parallel processing.
· “Secure and Parallel Determinant Computation for Large-Scale Matrices in Edge Environments”
A shared numerical linear algebra method works regardless of basis or monomial order and handles infinite positive-dimensional solution sets
