Yimin Shao | Searcharxiv

arXiv2026

Discovering Physically Interpretable Mathematical Expression for Predicting CO2 Adsorption in Metal-Organic Frameworks via Machine Learning-Symbolic Regression

This work presents a machine learning-symbolic regression (ML-SR) strategy to develop a physically interpretable formula for predicting low pressure CO2 adsorption capacity in hypothetical metal-organic frameworks (hMOFs). Four ML models were trained on a small dataset of 1,000 samples, and five key descriptors-largest cavity diameter, pore limiting diameter, void fraction, gravimetric surface area, and number of hydrogen atoms-were identified through SHAP and feature importance analyses. Symbolic regression was then employed to derive a concise adsorption formula, Q=aA, where a represents an adsorption baseline (mmol/g) and A is a dimensionless adsorption number incorporating four structural descriptors. We interpret A as the ratio between an adsorption binding force and a diffusion driving force, revealing how pore topology and surface chemistry jointly influence adsorption. Validation against a comprehensive dataset of 137,652 hMOFs demonstrates that this formula achieves over 70% prediction accuracy for 62,448 structures, confirming strong applicability within defined structural and operational ranges. Unlike conventional black box ML models, the proposed physics-guided expression enables efficient prediction and provides clearer insight into adsorption mechanisms.

cond-mat.mtrl-sci↗

arXiv2022

Slow-varying Dynamics Assisted Temporal Capsule Network for Machinery Remaining Useful Life Estimation

Capsule network (CapsNet) acts as a promising alternative to the typical convolutional neural network, which is the dominant network to develop the remaining useful life (RUL) estimation models for mechanical equipment. Although CapsNet comes with an impressive ability to represent the entities' hierarchical relationships through a high-dimensional vector embedding, it fails to capture the long-term temporal correlation of run-to-failure time series measured from degraded mechanical equipment. On the other hand, the slow-varying dynamics, which reveals the low-frequency information hidden in mechanical dynamical behaviour, is overlooked in the existing RUL estimation models, limiting the utmost ability of advanced networks. To address the aforementioned concerns, we propose a Slow-varying Dynamics assisted Temporal CapsNet (SD-TemCapsNet) to simultaneously learn the slow-varying dynamics and temporal dynamics from measurements for accurate RUL estimation. First, in light of the sensitivity of fault evolution, slow-varying features are decomposed from normal raw data to convey the low-frequency components corresponding to the system dynamics. Next, the long short-term memory (LSTM) mechanism is introduced into CapsNet to capture the temporal correlation of time series. To this end, experiments conducted on an aircraft engine and a milling machine verify that the proposed SD-TemCapsNet outperforms the mainstream methods. In comparison with CapsNet, the estimation accuracy of the aircraft engine with four different scenarios has been improved by 10.17%, 24.97%, 3.25%, and 13.03% concerning the index root mean squared error, respectively. Similarly, the estimation accuracy of the milling machine has been improved by 23.57% compared to LSTM and 19.54% compared to CapsNet.

cs.LG↗