Computational Mathematics for and with AI/ML

Companion page for our group poster at the Math & AI workshop in Seattle (August 18-20, 2026).

This page accompanies our poster at the Math & AI Summer in Seattle workshop (August 18-20, 2026), which brings together the themes of the DARPA expMath and AIQ programs. The map below is the poster's centerpiece: every box is a link to the corresponding paper, library, or note, and the application papers from the poster's bottom strip follow underneath.

Applications Foundations Mathematics for AI AI for Mathematics THEORY OF AI MODELS AI SOLVES SCIENCE PROBLEMS KERNELS & STANDARDS AI RUNS ON AI WRITES & CHECKS MATH RandBLAS and RandLAPACK randomized matrix computation libraries on GitHub RandBLAS + RandLAPACK randomized matrix computation libraries RandRAND randomized preconditioning paper on arXiv RandRAND randomized preconditioning PRISM spectrum-aware matrix iterations paper on arXiv PRISM spectrum-aware matrix iterations AutoSpec automated discovery of numerical algorithms paper on arXiv AutoSpec automated numerical algorithms RL4RLA paper on arXiv RL4RLA teaching ML to discover RandNLA algorithms VERITAS: description below on this page VERITAS automated testing & certification of AI-generated NLA code VSCL: description below on this page VSCL machine-checked numerical stability proofs in Lean Heavy-tailed self-regularization paper on arXiv HTSR weight matrix spectral self-regularization HTMuon paper on arXiv; RMNP linked in the index below HTMuon | RMNP matrix-based optimizers AlphaQ paper on arXiv; KVQuant and SqueezeLLM linked in the index below AlphaQ | KVQuant | SqueezeLLM quantization Models of heavy-tailed mechanistic universality paper on arXiv Heavy-tailed Random Matrix Models spectral properties of trained neural networks Powerformer recency-biased causal attention paper on arXiv Powerformer power-law causal attention FLARE epistemic uncertainty in diffusion models paper on arXiv FLARE uncertainty estimation NeurDE neural equilibria for conservation laws paper on arXiv NeurDE neural conservation laws Score-based generative modeling through stochastic differential equations paper on arXiv (reference, not ours) Mathematics of Diffusion Models Neural ordinary differential equations paper on arXiv (reference, not ours) Neural ODEs Fourier neural operator paper on arXiv; PINNs linked in the index below (reference, not ours) Neural Operators | Physics-Informed Neural Networks (PINNs) DeepMind AlphaProof announcement (reference, not ours) AlphaProof IEEE P3109 working group page (reference, not ours) IEEE Low-Precision Arithmetic Standards BLAS and LAPACK at Netlib (reference, not ours) BLAS | LAPACK Lean mathlib4 on GitHub (reference, not ours) Lean Formalization of Mathematics our recent projects familiar reference (not ours) planned integration

All projects on the map

VERITAS

VERITAS (Verification Engine for Reliable and Intelligent Testing of Algebra Systems) is our framework for automated testing and certification of AI-generated numerical linear algebra code: LLM recognition and behavioural fingerprinting route any kernel to a testing harness covering correctness, reproducibility, performance, and uncertainty, ending in a certificate of trust. The project is in its pre-award phase and has no public artifact yet; this entry will link to it when one exists.

VSCL

The Verified Scientific Computing Library (VSCL) is a Lean 4 library of machine-checked numerical stability proofs in the style of Higham's error analysis, built so that AI-generated numerical mathematics can be verified at the speed it is generated. A public release is being consolidated; this entry will link to the repository when it lands.

Application papers

Real problems we have solved, from the poster's bottom strip:

Model Quality Diagnostics
HTSR I: arXiv:1810.01075 · HTSR II: arXiv:2002.06716
Time Series Foundation Model
Chronos: arXiv:2403.07815
Chemistry Foundation Model
MIST: arXiv:2510.18900
LLM for Material Science
MatterChat: arXiv:2502.13107
Conservation Law Simulation
NeurDE: arXiv:2501.06933
Earthquake Simulation
CGM-GM: arXiv:2407.15089
Earthquake Forecast
WaveCastNet: arXiv:2405.20516
Weather Emulation
paper: arXiv:2603.25687
Chemical Property Prediction
chemrxiv.10001648
Supply Chain Optimization
Consensus Planning: arXiv:2408.16462

Poster by Shenghao Yang, Maksim Melnichenko, and Oleg Balabanov. PI: Michael Mahoney (UCB/ICSI/LBNL); co-PIs: Ben Erichson (ICSI/LBNL), Yaoqing Yang (Dartmouth), Yujun Yang (Dartmouth). Page maintained by Maksim Melnichenko.