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Scientific equation discovery and symbolic regression using LLMs, combining code generation with evolutionary search (ICLR 2025 Oral)

Kolmogorov-Arnold Networks with learnable activation functions on edges instead of fixed node activations, achieving strong performance in function fitting, PDE solving, and scientific discovery with enhanced interpretability as an alternative to MLPs (MIT, 16.3K+ stars, 2024)

Learning nonlinear operators

Sparse identification of nonlinear dynamics

High-performance symbolic regression for discovering interpretable scientific equations from data, multi-population evolutionary search with Python/Julia backend, widely used in physics and astronomy (Cambridge, NeurIPS 2023)

Parallel symbolic regression network evaluating millions of expressions on GPU with automated subtree reuse, Nature Computational Science cover article (MIT, 2026)

Learning operators in Fourier space

Efficient foundation models for PDEs with pretrained transformer-based neural operators and downstream task fine-tuning pipelines, HuggingFace integration for models and datasets (ETH Zurich CAMLab, arXiv 2024)

Geometry Aware Operator Transformer serving as an efficient and accurate neural surrogate for PDEs on arbitrary domains, combining geometric priors with transformer architectures for scientific computing (ETH Zurich CAMLab, 92+ stars)

Differentiable PDE solving framework for machine learning with built-in fluid simulation, supporting PyTorch/JAX/TensorFlow backends and enabling neural network training within physical simulations (TUM, MIT License)

Efficient differentiable n-dimensional PDE solvers built on JAX and Equinox, shipping 46+ built-in equations with Fourier spectral methods, exponential time differencing, and full auto-differentiation for physics-based deep learning workflows (MIT, 200+ stars, 2024)