Proves that Rademacher complexity of depth-d compositional trees over finite operator vocabulary is controlled by (K b L)^{d} / sqrt(n) under Lipschitz conditions on operators.
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A convex neural network is trained inside an elastoplastic stress integration loop using force equilibrium losses to identify yield functions from full-field displacement data.
DRSR uses Quality-Diversity to produce diverse symbolic regression expressions differing in residual distributions, enabling post-search selection on synthetic and astronomical data.
A finite sheaf-theoretic framework ranks obstruction measures to identify when an AI agent's theory must deform within its language or extend to a new one, validated on a controlled transition benchmark.
AI CFD Scientist autonomously discovers a Spalart-Allmaras runtime correction reducing lower-wall Cf RMSE by 7.89% on the periodic hill at Reh=5600 while using a vision-language gate to detect 14 of 16 silent failures missed by solver checks.
Latent Grammar Flow discovers ODEs by placing grammar-based equation representations in a discrete latent space, using a behavioral loss to cluster similar equations, and sampling via a discrete flow model guided by data fit and constraints.
In-context symbolic regression methods improve robustness of symbolic formula recovery from KANs, cutting median OFAT test MSE by up to 99.8 percent across hyperparameter sweeps.
Symbolic rational-function networks recover an admissible PDE from noiseless complete measurements and select the regularization-minimizing parameterization within the architecture.
AlphaEvolve is an LLM-orchestrated evolutionary coding agent that discovered a 4x4 complex matrix multiplication algorithm using 48 scalar multiplications, the first improvement over Strassen's algorithm in 56 years, plus optimizations for Google data centers and hardware.
AutoSINDy automatically builds a tailored basis library from PySR symbolic regression and applies SINDy to recover ground-truth nonlinear dynamics with 92.8% success under noise.
DoLQ employs a sampler agent, parameter optimizer, and LLM-based scientist agent to iteratively propose, refine, and evaluate ODE candidates, yielding higher success rates and better symbolic term recovery than prior symbolic regression methods on multi-dimensional benchmarks.
ViSA-R2 recovers single executable SymPy expressions for linear steady-state fields from visualizations using a self-verifying chain-of-thought that recognizes patterns, hypothesizes solution families, derives parameters, and checks consistency.
WSINDYc-MPC identifies governing dynamics more robustly than benchmarks under high noise, enabling longer prediction horizons and lower tracking errors in fusion, drone, chaos, and aircraft control tasks.
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AI CFD Scientist: Toward Open-Ended Computational Fluid Dynamics Discovery with Physics-Aware AI Agents
AI CFD Scientist autonomously discovers a Spalart-Allmaras runtime correction reducing lower-wall Cf RMSE by 7.89% on the periodic hill at Reh=5600 while using a vision-language gate to detect 14 of 16 silent failures missed by solver checks.