Sparse discovery of differential equations based on multi-fidelity Gaussian process

• URL: http://arxiv.org/abs/2401.11825v1
• Date: Mon, 22 Jan 2024 10:38:14 GMT
• Title: Sparse discovery of differential equations based on multi-fidelity Gaussian process
• Authors: Yuhuang Meng and Yue Qiu
• Abstract summary: Sparse identification of differential equations aims to compute the analytic expressions from the observed data explicitly. It exhibits sensitivity to the noise in the observed data, particularly for the derivatives computations. Existing literature predominantly concentrates on single-fidelity (SF) data, which imposes limitations on its applicability. We present two novel approaches to address these problems from the view of uncertainty quantification.
• Score: 0.8088384541966945
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sparse identification of differential equations aims to compute the analytic expressions from the observed data explicitly. However, there exist two primary challenges. Firstly, it exhibits sensitivity to the noise in the observed data, particularly for the derivatives computations. Secondly, existing literature predominantly concentrates on single-fidelity (SF) data, which imposes limitations on its applicability due to the computational cost. In this paper, we present two novel approaches to address these problems from the view of uncertainty quantification. We construct a surrogate model employing the Gaussian process regression (GPR) to mitigate the effect of noise in the observed data, quantify its uncertainty, and ultimately recover the equations accurately. Subsequently, we exploit the multi-fidelity Gaussian processes (MFGP) to address scenarios involving multi-fidelity (MF), sparse, and noisy observed data. We demonstrate the robustness and effectiveness of our methodologies through several numerical experiments.

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