Syncing Optimization of Dimensionality Reduction and Inversion Via Coupled Autoencoder

Abstract

Abstract. Acquiring reliable key parameters is essential for high-performance optimization of mechanical equipment. When direct measurement is infeasible, parameters are inferred by inverse methods from measurable high-dimensional responses. However, such data often contain redundancy, and dimensionality reduction may compromise credibility, leading to decreased accuracy and stability of the inferred parameters. To address this issue, a coupled autoencoder inverse method (CAIM) is proposed in this study. A neural network is constructed to couple the autoencoder with the inverse solver, enabling synchronous optimization of dimensionality reduction and parameter inversion via composite loss integrating reconstruction and inversion errors. The bottleneck dimension of the autoencoder is determined by the cumulative variance contribution rate from principal component analysis to preserve key information with minimal dimensions. A dynamic adaptive weighting strategy based on Bayesian optimization balances generalization and inversion accuracy. The proposed CAIM framework is validated on a composite laminated plate, achieving maximum error below 1% with sufficient samples, which registers significantly superior accuracy to those by guidance constraint autoencoder-inverse neural network (GAE-INN) and autoencoder (AE)-INN. With only 80 training samples, CAIM maintains errors below 5%, whereas the original INN requires over 500 samples for similar accuracy. The results demonstrate that CAIM ensures high reliability and efficiency, effectively overcoming the long-standing instability issue of conventional inverse methods due to dimensionality reduction.