Manifold-adapted anisotropic radial basis functions, shaped by clustering, yield a global explicit non-intrusive reduced vector field that recovers chaotic invariant measures competitively with intrusive and neural models.
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Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach
8 Pith papers cite this work, alongside 1,290 external citations. Polarity classification is still indexing.
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representative citing papers
Projecting the self-supervised ESN loss onto the input subspace yields an online perturbation rule with O(n_in) variance instead of O(n_r^2)/O(n_r), with the orthogonal residual removed by a static map.
Evolutionary selection on reservoir size, connectivity, spectral radius, input scaling, and regularization for Kuramoto-Sivashinsky forecasting reveals a conserved stochastic-block-model spectral envelope, locked intermediate modularity, and a horizontal cost-modularity floor in elite architectures.
PIDM-DP integrates Dormand-Prince ODE solving into DDPM denoising with scheduled physics guidance to reconstruct chaotic states, reporting up to 15.4x RMSE gains over baselines on five systems including stiff cases.
Mechanism learning infers active local evolution rules via prototype-anchored descriptors to achieve more robust forecasting than direct state prediction on benchmarks like Burgers, WeatherBench2, and Lorenz96.
A dynamics-informed Temporal Fusion Transformer surrogate emulates stochastic tipping events in global ocean transport simulations with 465x speedup and high-fidelity timing predictions.
Optimizing eigenvalues of the adjacency matrix in linear reservoir computers yields better training and test performance than random linear reservoirs and often beats comparable nonlinear ones.
Comparative experiments on three chaotic systems find that architectures using integrator-like updates exhibit lower bias, reduced perturbation amplification, and more stable long-horizon rollouts than other common designs when model capacity is matched.
citing papers explorer
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Manifold-adapted radial basis functions for reduced-order modelling of chaotic flows
Manifold-adapted anisotropic radial basis functions, shaped by clustering, yield a global explicit non-intrusive reduced vector field that recovers chaotic invariant measures competitively with intrusive and neural models.
-
Scalable Perturbation Learning for Online Self-Supervised Learning in Echo State Networks
Projecting the self-supervised ESN loss onto the input subspace yields an online perturbation rule with O(n_in) variance instead of O(n_r^2)/O(n_r), with the orthogonal residual removed by a static map.
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Evolutionary Optimization Reveals Structural Constraints on Reservoir Architecture for Spatiotemporal Chaos
Evolutionary selection on reservoir size, connectivity, spectral radius, input scaling, and regularization for Kuramoto-Sivashinsky forecasting reveals a conserved stochastic-block-model spectral envelope, locked intermediate modularity, and a horizontal cost-modularity floor in elite architectures.
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PIDM-DP: Physics-Informed Diffusion with Dormand-Prince Integration for Chaotic System Identification and State Reconstruction across Multiple Dynamical Regimes
PIDM-DP integrates Dormand-Prince ODE solving into DDPM denoising with scheduled physics guidance to reconstruct chaotic states, reporting up to 15.4x RMSE gains over baselines on five systems including stiff cases.
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Mechanism Learning: Prototype-Anchored Mechanism Inference for Scientific Forecasting
Mechanism learning infers active local evolution rules via prototype-anchored descriptors to achieve more robust forecasting than direct state prediction on benchmarks like Burgers, WeatherBench2, and Lorenz96.
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Deep Learning Surrogates for Emulating Stochastic Climate Tipping Dynamics
A dynamics-informed Temporal Fusion Transformer surrogate emulates stochastic tipping events in global ocean transport simulations with 465x speedup and high-fidelity timing predictions.
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Optimizing the Network Topology of a Linear Reservoir Computer
Optimizing eigenvalues of the adjacency matrix in linear reservoir computers yields better training and test performance than random linear reservoirs and often beats comparable nonlinear ones.
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A comparative study of accuracy and rollout stability of temporal surrogate models
Comparative experiments on three chaotic systems find that architectures using integrator-like updates exhibit lower bias, reduced perturbation amplification, and more stable long-horizon rollouts than other common designs when model capacity is matched.