Physics-informed Spline Learning for Nonlinear Dynamics Discovery

@inproceedings{Sun2021PhysicsinformedSL,
  title={Physics-informed Spline Learning for Nonlinear Dynamics Discovery},
  author={Fangzheng Sun and Yang Liu and Hao Sun},
  booktitle={IJCAI},
  year={2021}
}
Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate science, engineering and social science. To address this fundamental challenge, we propose a novel Physicsinformed Spline Learning (PiSL) framework to discover parsimonious governing equations for nonlinear dynamics, based on sparsely sampled noisy data. The… 

Figures and Tables from this paper

Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search
TLDR
A novel Symbolic Physics Learner (SPL) machine is proposed to discover the mathematical structure of nonlinear dynamics, to interpret mathematical operations and system state variables by computational rules and symbols, establish symbolic reasoning of mathematical formulas via expression trees, and employ a Monte Carlo tree search (MCTS) agent to explore optimal expression trees based on measurement data.
Discovering Governing Equations by Machine Learning implemented with Invariance
TLDR
Comparing the results with PDE-NET in numerical experiments of Burgers equation and Sine-Gordon equation, it shows that the method presented in this study has better accuracy, parsimony, and interpretability.
Simultaneous Identification and Denoising of Dynamical Systems
TLDR
An algorithm for Simultaneous Identification and Denoising of a Dynamical System (SIDDS) that infer the noise in the state measurements by requiring that the denoised data satisfies the dynamical system with an equality constraint and can correctly identify the sparsity structure for higher levels of noise than existing techniques.
Physics-Informed Graph Learning: A Survey
TLDR
This paper presents a systematic review of PIGL methods, beginning with introducing a unified framework of graph learning models, and then examining existing P IGL methods in relation to the unified framework.
Controlling Chaos in Van Der Pol Dynamics Using Signal-Encoded Deep Learning
TLDR
This work introduces Physics-Informed Deep Operator Control (PIDOC), and by encoding the control signal and initial position into the losses of a physics-informed neural network (PINN), the nonlinear system is forced to exhibit the desired trajectory given theControl signal.
A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study
TLDR
This work investigates and compares the performance of several local and global smoothing techniques to denoise the state measurements and numerically estimate the state time-derivatives to improve the accuracy and robustness of two sparse regression methods to recover governing equations: Sequentially Thresholded Least Squares and Weighted Basis Pursuit Denoising algorithms.
Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning
TLDR
This work proposes a novel physics-encoded discrete learning framework for discovering spatiotemporal PDEs from scarce and noisy data and introduces a novel deep convolutional-recurrent network that can encode prior physics knowledge while remaining flexible on representation capability.
Physics-Informed Deep Operator Control: Controlling chaos in van der Pol oscillating circuits
TLDR
PIDOC is introduced, by encoding control signal and initial position into the losses of a Physics-Informed Neural Network (PINN), the nonlinear system exhibits the desired route given the control signal.
Uncovering Closed-form Governing Equations of Nonlinear Dynamics from Videos
TLDR
A novel end-to-end unsupervised deep learning framework to uncover the mathematical structure of equations that governs the dynamics of moving objects in videos and enables discovery of parsimonious interpretable model in a flexible and accessible sensing environment where only videos are available.

References

SHOWING 1-10 OF 45 REFERENCES
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
TLDR
This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning and using sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data.
Data Set and Reference Models of EMPS
TLDR
The EMPS has a pure integrator, is piloted by a controller consisting of two nested loops and exhibits an asymmetrical friction, which constitutes a challenge when performing identification of such electro-mechanical systems.
Learning beyond simulated physics
Most advancements in terms of time-series predictions of physical systems is based 1 on simulated physics. Thus we are proposing a new dataset based on videos of 2 a real-world, chaotic double
Science Advances
IT is not easy to discern the relevance of the title to the series of essays which Prof. J. B. S. Haldane has collected in this book. They cover a wide field. Some rather scrappy biographical
Data-driven discovery of partial differential equations
TLDR
The sparse regression method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation.
Distilling Free-Form Natural Laws from Experimental Data
TLDR
This work proposes a principle for the identification of nontriviality, and demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula, and discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation.
Physics-informed learning of governing equations from scarce data
TLDR
The efficacy and robustness of this method are demonstrated, both numerically and experimentally, on discovering a variety of partial differential equation systems with different levels of data scarcity and noise accounting for different initial/boundary conditions.
SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics
TLDR
This work develops Sindy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities and demonstrates the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data.
Data-driven discovery of governing equations for fluid dynamics based on molecular simulation
TLDR
This work proves that data-driven discovery combined with molecular simulations is a promising and alternative method to derive governing equations in fluid dynamics, and it is expected to pave a new way to establish the governing equations of non-equilibrium flows and complex fluids.
Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery
TLDR
This article uses a neural network-based architecture for symbolic regression called the equation learner (EQL) network and integrates it with other deep learning architectures such that the whole system can be trained end-to-end through backpropagation.
...
...