Probabilistic Gradients for Fast Calibration of Differential Equation Models
| Autor: | Jonathan Cockayne, Andrew B. Duncan |
|---|---|
| Přispěvatelé: | The Alan Turing Institute |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics
Interdisciplinary Applications FOS: Computer and information sciences Statistics and Probability Computer Science - Machine Learning probabilistic numerics Calibration (statistics) Computer science Machine Learning (stat.ML) SENSITIVITY-ANALYSIS 010103 numerical & computational mathematics 01 natural sciences Statistics - Computation Bottleneck Machine Learning (cs.LG) Methodology (stat.ME) sensitivity analysis Statistics - Machine Learning FOS: Mathematics Discrete Mathematics and Combinatorics Applied mathematics Mathematics - Numerical Analysis 0101 mathematics Mathematics - Optimization and Control Computation (stat.CO) Statistics - Methodology Science & Technology Physics 0103 Numerical and Computational Mathematics Applied Mathematics 0104 Statistics Probabilistic logic Experimental data Numerical Analysis (math.NA) Physics Mathematical EMULATION 010101 applied mathematics Differential equation models REDUCTION Optimization and Control (math.OC) Modeling and Simulation Physical Sciences Statistics Probability and Uncertainty Applied science Mathematics PDE constrained optimization |
| Popis: | Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the calculation of local sensitivities, i.e. derivatives of the loss function with respect to the estimated parameters, which often necessitates several numerical solves of the underlying system of partial or ordinary differential equations. In this paper we present a new probabilistic approach to computing local sensitivities. The proposed method has several advantages over classical methods. Firstly, it operates within a constrained computational budget and provides a probabilistic quantification of uncertainty incurred in the sensitivities from this constraint. Secondly, information from previous sensitivity estimates can be recycled in subsequent computations, reducing the overall computational effort for iterative gradient-based calibration methods. The methodology presented is applied to two challenging test problems and compared against classical methods. |
| Databáze: | OpenAIRE |
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