Physics-Driven ML-Based Modelling for Correcting Inverse Estimation

TL;DR

This paper introduces GEESE, a physics-driven machine learning framework that detects and corrects failed inverse estimations in science and engineering, improving accuracy and efficiency by integrating physical laws with neural network models.

Contribution

The paper presents GEESE, a novel hybrid neural network approach combining error modeling and generative models to enhance inverse problem solving in SAE domains.

Findings

GEESE reduces the number of failed estimations compared to existing methods.

It requires fewer physical evaluations, increasing efficiency.

GEESE demonstrates superior performance on real-world SAE inverse problems.

Abstract

When deploying machine learning estimators in science and engineering (SAE) domains, it is critical to avoid failed estimations that can have disastrous consequences, e.g., in aero engine design. This work focuses on detecting and correcting failed state estimations before adopting them in SAE inverse problems, by utilizing simulations and performance metrics guided by physical laws. We suggest to flag a machine learning estimation when its physical model error exceeds a feasible threshold, and propose a novel approach, GEESE, to correct it through optimization, aiming at delivering both low error and high efficiency. The key designs of GEESE include (1) a hybrid surrogate error model to provide fast error estimations to reduce simulation cost and to enable gradient based backpropagation of error feedback, and (2) two generative models to approximate the probability distributions of the candidate states for simulating the exploitation and exploration behaviours. All three models are constructed as neural networks. GEESE is tested on three real-world SAE inverse problems and compared to a number of state-of-the-art optimization/search approaches. Results show that it fails the least number of times in terms of finding a feasible state correction, and requires physical evaluations less frequently in general.