Manifold embedding data-driven mechanics

Bahmani, Bahador; Sun, WaiChing

doi:10.1016/j.jmps.2022.104927

Cited by 19 publications

(5 citation statements)

References 83 publications

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“…[66][67][68] Some studies formulate the learning of constitutive laws as a manifold learning problem, searching for the response surface rather than using conventional surrogate models for input-to-output mapping. [69][70][71][72][73]…”

Section: Reviews On Interpretable Machine Learning Constitutive Lawsmentioning

confidence: 99%

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Physics‐constrained symbolic model discovery for polyconvex incompressible hyperelastic materials

Bahmani,

Sun

2024

Numerical Meth Engineering

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We present a machine learning framework capable of consistently inferring mathematical expressions of hyperelastic energy functionals for incompressible materials from sparse experimental data and physical laws. To achieve this goal, we propose a polyconvex neural additive model (PNAM) that enables us to express the hyperelastic model in a learnable feature space while enforcing polyconvexity. An upshot of this feature space obtained via the PNAM is that (1) it is spanned by a set of univariate basis functions that can be re‐parametrized with a more complex mathematical form, and (2) the resultant elasticity model is guaranteed to fulfill the polyconvexity, which ensures that the acoustic tensor remains elliptic for any deformation. To further improve the interpretability, we use genetic programming to convert each univariate basis into a compact mathematical expression. The resultant multi‐variable mathematical models obtained from this proposed framework are not only more interpretable but are also proven to fulfill physical laws. By controlling the compactness of the learned symbolic form, the machine learning‐generated mathematical model also requires fewer arithmetic operations than its deep neural network counterparts during deployment. This latter attribute is crucial for scaling large‐scale simulations where the constitutive responses of every integration point must be updated within each incremental time step. We compare our proposed model discovery framework against other state‐of‐the‐art alternatives to assess the robustness and efficiency of the training algorithms and examine the trade‐off between interpretability, accuracy, and precision of the learned symbolic hyperelastic models obtained from different approaches. Our numerical results suggest that our approach extrapolates well outside the training data regime due to the precise incorporation of physics‐based knowledge.

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Section: Reviews On Interpretable Machine Learning Constitutive Lawsmentioning

confidence: 99%

“…Following the WYPIWYG idea, methods based on spline shape functions are also introduced 66–68 . Some studies formulate the learning of constitutive laws as a manifold learning problem, searching for the response surface rather than using conventional surrogate models for input‐to‐output mapping 69–73 …”

Section: Introductionmentioning

confidence: 99%

Physics‐constrained symbolic model discovery for polyconvex incompressible hyperelastic materials

Bahmani,

Sun

2024

Numerical Meth Engineering

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“…Data‐driven (model‐free) approaches overcome such problems, and they become even more appealing due to development of full‐field measurement experimental techniques. Data‐driven computational mechanics is an actively developing area (see e.g., 3–6 and references therein), in particular, methods based on minimization of the distance between material states (experimental data) and mechanical states/constraint manifold have attracted many researchers 5,7,8,3,9 …”

Section: Introductionmentioning

confidence: 99%

“…Data-driven computational mechanics is an actively developing area (see e.g., [3][4][5][6] and references therein), in particular, methods based on minimization of the distance between material states (experimental data) and mechanical states/constraint manifold have attracted many researchers. 5,7,8,3,9 The main obstacle for data-driven approaches is the lack of independent experimental data and data sufficiency for describing mechanical behavior for different deformation modes. This is the common issue for any approach.…”

Section: Introductionmentioning

confidence: 99%

Interpretable data‐driven modeling of hyperelastic membranes

Salamatova

Liogky

2023

Numer Methods Biomed Eng

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We proposed an approach for interpretable data‐driven modeling of an isotropic incompressible hyperelastic membrane deformation. The approach is based on the response functions in terms of the Laplace stretch and the finite element method, where response functions are partial derivatives of a hyperelastic potential with respect to the chosen strain measure. The Laplace stretch as the strain measure allows us to recover directly the response functions from experimental data and construct automatically data‐driven constitutive relations. All needed formulas were obtained explicitly. We tested our approach for membrane inflation with data‐driven constitutive relations based on the perforated membrane extension tests.

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“…This paradigm has been applied to other engineering problems, such as nonlinear material modeling [ 22 , 24 , 25 ] and, fracture mechanics [ 26 ], among others. Furthermore, deep manifold embedding techniques have been introduced in data-driven computing for extracting low-dimensional feature space [ 27 , 28 ].…”

Section: Introductionmentioning

confidence: 99%

A Feature-Encoded Physics-Informed Parameter Identification Neural Network for Musculoskeletal Systems

Taneja

et al. 2022

Journal of Biomechanical Engineering

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Identification of muscle-tendon force generation properties and muscle activities from physiological measurements, e.g., motion data and raw surface electromyography (sEMG), offers the opportunities for construction of a subject-specific musculoskeletal (MSK) digital twin system for health conditions assessment and human motion prediction. While machine learning approaches with capabilities in extracting complex features and patterns from large amount of data have been applied to motion prediction given sEMG signals, the learnt data-driven mapping is black-box and may not satisfy the underlying physics. In this work, we propose a feature encoded physics-informed parameter identification neural network (FEPI-PINN) for simultaneous prediction of motion and parameter identification of human MSK systems. Features of the high-dimensional noisy muscle excitation sEMG signals are used to construct a low-dimensional representation for enhancement of forward dynamics prediction. A physics-informed neural network is trained to relate sEMG signals to motion in the low dimensional feature space and simultaneously identify key MSK parameters. The numerical examples demonstrate that the proposed framework can effectively identify subject-specific muscle parameters, and the trained physics-informed forward-dynamics surrogate yields motion prediction of elbow flexion-extension motion in good agreement with the measured joint motion data.

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Manifold embedding data-driven mechanics

Cited by 19 publications

References 83 publications

Physics‐constrained symbolic model discovery for polyconvex incompressible hyperelastic materials

Physics‐constrained symbolic model discovery for polyconvex incompressible hyperelastic materials

Interpretable data‐driven modeling of hyperelastic membranes

A Feature-Encoded Physics-Informed Parameter Identification Neural Network for Musculoskeletal Systems

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