SINDy-BVP: Sparse identification of nonlinear dynamics for boundary value problems
We develop a data-driven model discovery and system identification technique for spatially-dependent boundary value problems (BVPs). Specifically, we leverage the sparse identification of nonlinear dynamics (SINDy) algorithm and group sparse regression techniques with a set of forcing functions and...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2021-06-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.023255 |
| _version_ | 1797211022869659648 |
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| author | Daniel E. Shea Steven L. Brunton J. Nathan Kutz |
| author_facet | Daniel E. Shea Steven L. Brunton J. Nathan Kutz |
| author_sort | Daniel E. Shea |
| collection | DOAJ |
| description | We develop a data-driven model discovery and system identification technique for spatially-dependent boundary value problems (BVPs). Specifically, we leverage the sparse identification of nonlinear dynamics (SINDy) algorithm and group sparse regression techniques with a set of forcing functions and corresponding state variable measurements to yield a parsimonious model of heterogeneous material systems. The technique models forced systems governed by linear or nonlinear operators of the form L[u(x)]=f(x) on a prescribed domain x∈[a,b]. We demonstrate the approach on a range of example systems, including Sturm-Liouville operators, beam theory (elasticity), and a class of nonlinear BVPs. The generated data-driven model is used to infer the governing operator and spatially-dependent parameters that describe the heterogenous, physical quantities of the system. Our SINDy-BVP framework enables the characterization of a broad range of systems, including for instance, the discovery of anisotropic materials with heterogeneous variability. |
| first_indexed | 2024-04-24T10:19:53Z |
| format | Article |
| id | doaj.art-dd3e4bc1db4441c19e09f2b9d7085dcf |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:19:53Z |
| publishDate | 2021-06-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-dd3e4bc1db4441c19e09f2b9d7085dcf2024-04-12T17:11:13ZengAmerican Physical SocietyPhysical Review Research2643-15642021-06-013202325510.1103/PhysRevResearch.3.023255SINDy-BVP: Sparse identification of nonlinear dynamics for boundary value problemsDaniel E. SheaSteven L. BruntonJ. Nathan KutzWe develop a data-driven model discovery and system identification technique for spatially-dependent boundary value problems (BVPs). Specifically, we leverage the sparse identification of nonlinear dynamics (SINDy) algorithm and group sparse regression techniques with a set of forcing functions and corresponding state variable measurements to yield a parsimonious model of heterogeneous material systems. The technique models forced systems governed by linear or nonlinear operators of the form L[u(x)]=f(x) on a prescribed domain x∈[a,b]. We demonstrate the approach on a range of example systems, including Sturm-Liouville operators, beam theory (elasticity), and a class of nonlinear BVPs. The generated data-driven model is used to infer the governing operator and spatially-dependent parameters that describe the heterogenous, physical quantities of the system. Our SINDy-BVP framework enables the characterization of a broad range of systems, including for instance, the discovery of anisotropic materials with heterogeneous variability.http://doi.org/10.1103/PhysRevResearch.3.023255 |
| spellingShingle | Daniel E. Shea Steven L. Brunton J. Nathan Kutz SINDy-BVP: Sparse identification of nonlinear dynamics for boundary value problems Physical Review Research |
| title | SINDy-BVP: Sparse identification of nonlinear dynamics for boundary value problems |
| title_full | SINDy-BVP: Sparse identification of nonlinear dynamics for boundary value problems |
| title_fullStr | SINDy-BVP: Sparse identification of nonlinear dynamics for boundary value problems |
| title_full_unstemmed | SINDy-BVP: Sparse identification of nonlinear dynamics for boundary value problems |
| title_short | SINDy-BVP: Sparse identification of nonlinear dynamics for boundary value problems |
| title_sort | sindy bvp sparse identification of nonlinear dynamics for boundary value problems |
| url | http://doi.org/10.1103/PhysRevResearch.3.023255 |
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