Learning mean-field equations from particle data using WSINDy
We develop a weak-form sparse identification method for interacting particle systems (IPS) with the primary goals of reducing computational complexity for large particle number N and offering robustness to either intrinsic or extrinsic noise. In particular, we use concepts from mean-field theory of IPS in combination with the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy) to provide a fast and reliable system identification scheme for recovering the governing stochastic differential equations for an IPS when the number of particles per experiment N is on the order of several thousands and the number of experiments M is less than 100. This is in contrast to existing work showing that system identification for N less than 100 and M on the order of several thousand is feasible using strong-form methods. We prove that under some standard regularity assumptions the scheme converges with rate O(N-1∕2) in the ordinary least squares setting and we demonstrate the convergence rate numerically on several systems in one and two spatial dimensions. Our examples include a canonical problem from homogenization theory (as a first step towards learning coarse-grained models), the dynamics of an attractive-repulsive swarm, and the IPS description of the parabolic-elliptic Keller-Segel model for chemotaxis. Code is available at https://github.com/MathBioCU/WSINDy_IPS.
| Medienart: |
E-Artikel |
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| Erscheinungsjahr: |
2022 |
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| Erschienen: |
2022 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:439 |
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| Enthalten in: |
Physica D. Nonlinear phenomena - 439(2022) vom: 01. Nov. |
| Sprache: |
Englisch |
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| Beteiligte Personen: |
Messenger, Daniel A [VerfasserIn] |
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| Links: |
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| Themen: |
Data-driven modeling |
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| Anmerkungen: |
Date Revised 20.10.2023 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
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| doi: |
10.1016/j.physd.2022.133406 |
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| funding: |
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| Förderinstitution / Projekttitel: |
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| 500 | |a Date Revised 20.10.2023 | ||
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| 500 | |a Citation Status PubMed-not-MEDLINE | ||
| 520 | |a We develop a weak-form sparse identification method for interacting particle systems (IPS) with the primary goals of reducing computational complexity for large particle number N and offering robustness to either intrinsic or extrinsic noise. In particular, we use concepts from mean-field theory of IPS in combination with the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy) to provide a fast and reliable system identification scheme for recovering the governing stochastic differential equations for an IPS when the number of particles per experiment N is on the order of several thousands and the number of experiments M is less than 100. This is in contrast to existing work showing that system identification for N less than 100 and M on the order of several thousand is feasible using strong-form methods. We prove that under some standard regularity assumptions the scheme converges with rate O(N-1∕2) in the ordinary least squares setting and we demonstrate the convergence rate numerically on several systems in one and two spatial dimensions. Our examples include a canonical problem from homogenization theory (as a first step towards learning coarse-grained models), the dynamics of an attractive-repulsive swarm, and the IPS description of the parabolic-elliptic Keller-Segel model for chemotaxis. Code is available at https://github.com/MathBioCU/WSINDy_IPS | ||
| 650 | 4 | |a Journal Article | |
| 650 | 4 | |a Data-driven modeling | |
| 650 | 4 | |a Interacting particle systems | |
| 650 | 4 | |a Mean-field limit | |
| 650 | 4 | |a Sparse regression | |
| 650 | 4 | |a Weak form | |
| 700 | 1 | |a Bortz, David M |e verfasserin |4 aut | |
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