D-CIPHER: Discovery of Closed-form Partial Differential Equations
- URL: http://arxiv.org/abs/2206.10586v3
- Date: Wed, 29 Nov 2023 18:23:57 GMT
- Title: D-CIPHER: Discovery of Closed-form Partial Differential Equations
- Authors: Krzysztof Kacprzyk, Zhaozhi Qian, Mihaela van der Schaar
- Abstract summary: We propose D-CIPHER, which is robust to measurement artifacts and can uncover a new and very general class of differential equations.
We further design a novel optimization procedure, CoLLie, to help D-CIPHER search through this class efficiently.
- Score: 80.46395274587098
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Closed-form differential equations, including partial differential equations
and higher-order ordinary differential equations, are one of the most important
tools used by scientists to model and better understand natural phenomena.
Discovering these equations directly from data is challenging because it
requires modeling relationships between various derivatives that are not
observed in the data (equation-data mismatch) and it involves searching across
a huge space of possible equations. Current approaches make strong assumptions
about the form of the equation and thus fail to discover many well-known
systems. Moreover, many of them resolve the equation-data mismatch by
estimating the derivatives, which makes them inadequate for noisy and
infrequently sampled systems. To this end, we propose D-CIPHER, which is robust
to measurement artifacts and can uncover a new and very general class of
differential equations. We further design a novel optimization procedure,
CoLLie, to help D-CIPHER search through this class efficiently. Finally, we
demonstrate empirically that it can discover many well-known equations that are
beyond the capabilities of current methods.
Related papers
- A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEs [46.685771141109306]
We propose an autoregressive and data-driven method using the analogy with classical numerical solvers for time-dependent, parametric and (typically) nonlinear PDEs.
We show that by leveraging DR we can deliver not only more accurate predictions, but also a considerably lighter and faster Deep Learning model.
arXiv Detail & Related papers (2025-02-12T11:16:15Z) - Differentiable Programming for Differential Equations: A Review [36.67198631261628]
Differentiable programming is a cornerstone of modern scientific computing.
Differentiating functions based on the numerical solution of differential equations is non-trivial.
We provide a comprehensive review of existing techniques to compute derivatives of numerical solutions of differential equations.
arXiv Detail & Related papers (2024-06-14T03:54:25Z) - ConDiff: A Challenging Dataset for Neural Solvers of Partial Differential Equations [40.6591136324878]
We present ConDiff, a novel dataset for scientific machine learning.
ConDiff focuses on the parametric diffusion equation with space dependent coefficients, a fundamental problem in many applications of partial differential equations (PDEs)
This class of problems is not only of great academic interest, but is also the basis for describing various environmental and industrial problems.
In this way, ConDiff shortens the gap with real-world problems while remaining fully synthetic and easy to use.
arXiv Detail & Related papers (2024-06-07T07:35:14Z) - Towards true discovery of the differential equations [57.089645396998506]
Differential equation discovery is a machine learning subfield used to develop interpretable models.
This paper explores the prerequisites and tools for independent equation discovery without expert input.
arXiv Detail & Related papers (2023-08-09T12:03:12Z) - Discovering ordinary differential equations that govern time-series [65.07437364102931]
We propose a transformer-based sequence-to-sequence model that recovers scalar autonomous ordinary differential equations (ODEs) in symbolic form from time-series data of a single observed solution of the ODE.
Our method is efficiently scalable: after one-time pretraining on a large set of ODEs, we can infer the governing laws of a new observed solution in a few forward passes of the model.
arXiv Detail & Related papers (2022-11-05T07:07:58Z) - Symbolic Recovery of Differential Equations: The Identifiability Problem [52.158782751264205]
Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations.
We provide both necessary and sufficient conditions for a function to uniquely determine the corresponding differential equation.
We then use our results to devise numerical algorithms aiming to determine whether a function solves a differential equation uniquely.
arXiv Detail & Related papers (2022-10-15T17:32:49Z) - A Probabilistic State Space Model for Joint Inference from Differential
Equations and Data [23.449725313605835]
We show a new class of solvers for ordinary differential equations (ODEs) that phrase the solution process directly in terms of Bayesian filtering.
It then becomes possible to perform approximate Bayesian inference on the latent force as well as the ODE solution in a single, linear complexity pass of an extended Kalman filter.
We demonstrate the expressiveness and performance of the algorithm by training a non-parametric SIRD model on data from the COVID-19 outbreak.
arXiv Detail & Related papers (2021-03-18T10:36:09Z) - The data-driven physical-based equations discovery using evolutionary
approach [77.34726150561087]
We describe the algorithm for the mathematical equations discovery from the given observations data.
The algorithm combines genetic programming with the sparse regression.
It could be used for governing analytical equation discovery as well as for partial differential equations (PDE) discovery.
arXiv Detail & Related papers (2020-04-03T17:21:57Z)
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.