Efficiently training SciML models with derivative-informed training data using order truncated imaginary numbers

doi:10.1016/j.cma.2026.118789

Efficiently training SciML models with derivative-informed training data using order truncated imaginary numbers

2026-02-07

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Krishna Prasath Logakannan

DOI：10.1016/j.cma.2026.118789

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The SciML community constantly faces challenges in data acquisition, which often results in sparse data for training. Incorporating derivatives during training has been shown to improve predictions from learned models in cases with sparse data. However, acquiring training data derivatives and computing corresponding model derivatives during fitness evaluations significantly increases the time required for both steps, which mitigates the benefits of leveraging derivatives in practice. Additionally, these issues are increased with increasing derivative order. In this work, these training steps are accelerated by using a hypercomplex algebra method, Order Truncated Imaginary (OTI) numbers, for efficient and accurate acquisition and computation of the requisite derivatives. Also presented is an assessment of using derivatives of arbitrary order in the training of symbolic regression (SR) models, termed derivative-informed training data for genetic programming with SR (DITD-GPSR). The effectiveness of the DITD-GPSR method is demonstrated using an optimization test function, a nonlinear oscillatory function, and a thick-walled cylinder solid mechanics problem. The results show that the DITD-GPSR method commonly requires just 10% of the training data to achieve similar accuracy to conventional GPSR, and the DITD-GPSR evolves to the exact equations in far fewer evolution steps, up to 100 times in some cases. Implementing OTI numbers enabled the computation of higher-order derivatives with negligible increase in compute time compared to exponential growth using conventional auto-differentiation.

Keywords:

Symbolic Regression

Derivative-Informed Training Data

Genetic Programming

SciML

Order Truncated Imaginary Numbers

Efficiently training SciML models with derivative-informed training data using order truncated imaginary numbers

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