Deep Learning of the Evolution Operator Enables Forecasting of Out-of-Training Dynamics in Chaotic Systems
- URL: http://arxiv.org/abs/2502.20603v1
- Date: Fri, 28 Feb 2025 00:07:18 GMT
- Title: Deep Learning of the Evolution Operator Enables Forecasting of Out-of-Training Dynamics in Chaotic Systems
- Authors: Ira J. S. Shokar, Peter H. Haynes, Rich R. Kerswell,
- Abstract summary: We show that a deep learning emulator for chaotic systems can forecast phenomena absent from training data.<n>Using the Kuramoto-Sivashinsky and beta-plane turbulence models, we evaluate the emulator through scenarios probing the fundamental phenomena of both systems.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We demonstrate that a deep learning emulator for chaotic systems can forecast phenomena absent from training data. Using the Kuramoto-Sivashinsky and beta-plane turbulence models, we evaluate the emulator through scenarios probing the fundamental phenomena of both systems: forecasting spontaneous relaminarisation, capturing initialisation of arbitrary chaotic states, zero-shot prediction of dynamics with parameter values outside of the training range, and characterisation of dynamical statistics from artificially restricted training datasets. Our results show that deep learning emulators can uncover emergent behaviours and rare events in complex systems by learning underlying mathematical rules, rather than merely mimicking observed patterns.
Related papers
- A Mathematical Model of the Hidden Feedback Loop Effect in Machine Learning Systems [44.99833362998488]
We introduce a repeated learning process to jointly describe several phenomena attributed to unintended hidden feedback loops.
A distinctive feature of such repeated learning setting is that the state of the environment becomes causally dependent on the learner itself over time.
We present a novel dynamical systems model of the repeated learning process and prove the limiting set of probability distributions for positive and negative feedback loop modes.
arXiv Detail & Related papers (2024-05-04T17:57:24Z) - Extrapolating tipping points and simulating non-stationary dynamics of
complex systems using efficient machine learning [2.44755919161855]
We propose a novel, fully data-driven machine learning algorithm based on next-generation reservoir computing to extrapolate the bifurcation behavior of nonlinear dynamical systems.
In doing so, post-tipping point dynamics of unseen parameter regions can be simulated.
arXiv Detail & Related papers (2023-12-11T10:37:28Z) - Constraining Chaos: Enforcing dynamical invariants in the training of
recurrent neural networks [0.0]
We introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems.
The training enforces dynamical invariants--such as the Lyapunov exponent spectrum and fractal dimension--in the systems of interest, enabling longer and more stable forecasts when operating with limited data.
arXiv Detail & Related papers (2023-04-24T00:33:47Z) - Stabilizing Machine Learning Prediction of Dynamics: Noise and
Noise-inspired Regularization [58.720142291102135]
Recent has shown that machine learning (ML) models can be trained to accurately forecast the dynamics of chaotic dynamical systems.
In the absence of mitigating techniques, this technique can result in artificially rapid error growth, leading to inaccurate predictions and/or climate instability.
We introduce Linearized Multi-Noise Training (LMNT), a regularization technique that deterministically approximates the effect of many small, independent noise realizations added to the model input during training.
arXiv Detail & Related papers (2022-11-09T23:40:52Z) - Knowledge-based Deep Learning for Modeling Chaotic Systems [7.075125892721573]
This paper considers extreme events and their dynamics and proposes models based on deep neural networks, called knowledge-based deep learning (KDL)
Our proposed KDL can learn the complex patterns governing chaotic systems by jointly training on real and simulated data.
We validate our model by assessing it on three real-world benchmark datasets: El Nino sea surface temperature, San Juan Dengue viral infection, and Bjornoya daily precipitation.
arXiv Detail & Related papers (2022-09-09T11:46:25Z) - Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate
Model Predictive Trajectory Tracking [76.27433308688592]
Accurately modeling quadrotor's system dynamics is critical for guaranteeing agile, safe, and stable navigation.
We present a novel Physics-Inspired Temporal Convolutional Network (PI-TCN) approach to learning quadrotor's system dynamics purely from robot experience.
Our approach combines the expressive power of sparse temporal convolutions and dense feed-forward connections to make accurate system predictions.
arXiv Detail & Related papers (2022-06-07T13:51:35Z) - Capturing Actionable Dynamics with Structured Latent Ordinary
Differential Equations [68.62843292346813]
We propose a structured latent ODE model that captures system input variations within its latent representation.
Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
arXiv Detail & Related papers (2022-02-25T20:00:56Z) - Likelihood-Free Inference in State-Space Models with Unknown Dynamics [71.94716503075645]
We introduce a method for inferring and predicting latent states in state-space models where observations can only be simulated, and transition dynamics are unknown.
We propose a way of doing likelihood-free inference (LFI) of states and state prediction with a limited number of simulations.
arXiv Detail & Related papers (2021-11-02T12:33:42Z) - Using scientific machine learning for experimental bifurcation analysis
of dynamic systems [2.204918347869259]
This study focuses on training universal differential equation (UDE) models for physical nonlinear dynamical systems with limit cycles.
We consider examples where training data is generated by numerical simulations, whereas we also employ the proposed modelling concept to physical experiments.
We use both neural networks and Gaussian processes as universal approximators alongside the mechanistic models to give a critical assessment of the accuracy and robustness of the UDE modelling approach.
arXiv Detail & Related papers (2021-10-22T15:43:03Z) - Deep Bayesian Active Learning for Accelerating Stochastic Simulation [74.58219903138301]
Interactive Neural Process (INP) is a deep active learning framework for simulations and with active learning approaches.
For active learning, we propose a novel acquisition function, Latent Information Gain (LIG), calculated in the latent space of NP based models.
The results demonstrate STNP outperforms the baselines in the learning setting and LIG achieves the state-of-the-art for active learning.
arXiv Detail & Related papers (2021-06-05T01:31:51Z) - Using Data Assimilation to Train a Hybrid Forecast System that Combines
Machine-Learning and Knowledge-Based Components [52.77024349608834]
We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is noisy partial measurements.
We show that by using partial measurements of the state of the dynamical system, we can train a machine learning model to improve predictions made by an imperfect knowledge-based model.
arXiv Detail & Related papers (2021-02-15T19:56:48Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.