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.
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