Manifold Learning Based Data-Driven Modeling for Biological Tissues
Jiun-Shyan Chen, University of California, San Diego
Data-driven modeling is a hybrid approach that integrates universal physical laws with experimental material data directly to circumvent the necessity of using phenomenological constitutive models. A robust data-driven simulation approach based on manifold learning technique, termed locally convex data-driven (LCDD) computing, is formulated under the Galerkin meshfree framework to simulate heart valve tissues under finite deformation, where the material data from biaxial tests were employed. The proposed approach reconstructs a local material manifold with the convex hull based on the nearest experimental data to the given state, and seeks for the optimum solution via the projection onto the associated local manifold. This learning process of local data structure leads to less sensitivity to noisy data and convergence enhancement. For enhancing numerical efficiency, a penalty relaxation is further introduced to recast the local learning solver in the context of non-negative least squares that can be solved effectively. In addition, due to the inherent manifold learning properties, LCDD performs well for high-dimensional data sets that are relatively sparse in real-world engineering applications. The employment of meshfree approximation and discretization allows for a smooth transition of material properties at the interface of different biological material components and a better approximation of stress/strain fields in the data-driven solver due to the enhanced smoothness. The numerical results demonstrate the effectiveness of the proposed data-driven approach for modelling complex biological materials.
Jiun-Shyan Chen, University of California, San Diego
Data-driven modeling is a hybrid approach that integrates universal physical laws with experimental material data directly to circumvent the necessity of using phenomenological constitutive models. A robust data-driven simulation approach based on manifold learning technique, termed locally convex data-driven (LCDD) computing, is formulated under the Galerkin meshfree framework to simulate heart valve tissues under finite deformation, where the material data from biaxial tests were employed. The proposed approach reconstructs a local material manifold with the convex hull based on the nearest experimental data to the given state, and seeks for the optimum solution via the projection onto the associated local manifold. This learning process of local data structure leads to less sensitivity to noisy data and convergence enhancement. For enhancing numerical efficiency, a penalty relaxation is further introduced to recast the local learning solver in the context of non-negative least squares that can be solved effectively. In addition, due to the inherent manifold learning properties, LCDD performs well for high-dimensional data sets that are relatively sparse in real-world engineering applications. The employment of meshfree approximation and discretization allows for a smooth transition of material properties at the interface of different biological material components and a better approximation of stress/strain fields in the data-driven solver due to the enhanced smoothness. The numerical results demonstrate the effectiveness of the proposed data-driven approach for modelling complex biological materials.
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