gLaSDI: Parametric physics-informed greedy latent space dynamics identification

He, Xiaolong; Choi, Young-Soo; William, Fries,; Belof, Jonathan L.; Chen, Jiun‐Shyan

doi:10.1016/j.jcp.2023.112267

Cited by 10 publications

(2 citation statements)

References 81 publications

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“…In recent years, machine learning (ML) or deep-learning-based approaches have gained significant popularity for solving forward and inverse problems, attributed to their capability in effectively extracting complex features and patterns from data [ 21 ]. This has been successfully demonstrated in numerous engineering applications such as reduced-order modeling [ 22 – 26 ], and materials modeling [ 27 – 29 ], among others. Data-driven computing techniques that enforce constraints of conservation laws in the learning algorithms of a material database, have been developed in the field of computational mechanics [ 29 – 37 ].…”

Section: Introductionmentioning

confidence: 99%

“…Given information on muscle activations, the joint motion of a subject-specific MSK system can be obtained by solving a forward dynamics problem. Data-driven approaches for motion prediction have also been introduced to directly map the input sEMG signal to joint kinetics/kinematics, bypassing the forward dynamics equations and the need for parameter estimation [ 26 – 30 ]. However, the resulting ML-based surrogate models lack interpretability and may not satisfy the underlying physics.…”

Section: Introductionmentioning

confidence: 99%

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A multi-resolution physics-informed recurrent neural network: formulation and application to musculoskeletal systems

Taneja,

He,

et al. 2023

Comput Mech

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This work presents a multi-resolution physics-informed recurrent neural network (MR PI-RNN), for simultaneous prediction of musculoskeletal (MSK) motion and parameter identification of the MSK systems. The MSK application was selected as the model problem due to its challenging nature in mapping the high-frequency surface electromyography (sEMG) signals to the low-frequency body joint motion controlled by the MSK and muscle contraction dynamics. The proposed method utilizes the fast wavelet transform to decompose the mixed frequency input sEMG and output joint motion signals into nested multi-resolution signals. The prediction model is subsequently trained on coarser-scale input–output signals using a gated recurrent unit (GRU), and then the trained parameters are transferred to the next level of training with finer-scale signals. These training processes are repeated recursively under a transfer-learning fashion until the full-scale training (i.e., with unfiltered signals) is achieved, while satisfying the underlying dynamic equilibrium. Numerical examples on recorded subject data demonstrate the effectiveness of the proposed framework in generating a physics-informed forward-dynamics surrogate, which yields higher accuracy in motion predictions of elbow flexion–extension of an MSK system compared to the case with single-scale training. The framework is also capable of identifying muscle parameters that are physiologically consistent with the subject’s kinematics data.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A multi-resolution physics-informed recurrent neural network: formulation and application to musculoskeletal systems

Taneja,

He,

et al. 2023

Comput Mech

Self Cite

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Physics‐Informed Active Learning With Simultaneous Weak‐Form Latent Space Dynamics Identification

He,

Tran,

Bortz

et al. 2024

Numerical Meth Engineering

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The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high‐dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. To enhance robustness against noise, we incorporate the weak‐form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak‐form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent‐space dynamics of high‐dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced‐order modeling. Furthermore, the greedy physics‐informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time‐dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10 Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7 relative errors. Compared with the high‐fidelity models, WgLaSDI achieves 121 to 1779 speed‐up.

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