5月27日 (木) に、2019年度に計算工学大賞を受賞されたスペイン・カタルーニャ大学のAntonio Huerta教授、および2020年度に計算工学大賞を受賞された米国カリフォルニア大学のJ. S. Chen教授の特別講演を開催致します。 特別講演に引き続き、計算工学大賞授賞式を開催致します。
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From low to high-order approximations in surrogate models for parametric flows
Professor of Applied Mathematics, Laboratori de Càlcul Numèric (LaCàN), Universitat Politècnica de Catalunya, Barcelona, Spain
Daily industrial practice requires fast and robust strategies to solve computationally-demanding problems. Moreover, Computational Fluid Dynamics (CFD) simulations in industrial design and optimization procedures involve the exploration of large sets of admissible configurations. Parameters of interest may include boundary conditions, physical properties of the fluid and geometric configurations. Hence, efficient tools to solve multiple queries of the same flow problem are required. Surrogate models based on reduced order methods are commonly employed to ease the computational burden of such high-dimensional problems, allowing to efficiently perform parametric studies and to evaluate quantities of interest in real-time.
Two major issues will be discussed. On the one hand, the development of robust computational technologies to accurately reproduce complex flows. Novel advances for robust high-order and low order strategies in compressible and incompressible flows will be described. Special emphasis will be given to a unified framework for the treatment of Riemann solvers in high-order strategies and to the face-centered finite volume (FCFV) method that secures first-order accuracy for the stress tensor without the need for gradient reconstruction, thus being insensitive to cell distortion and stretching.
On the other hand, this talk reviews some recent contributions involving a priori and a posteriori surrogate models for the solution of parameterized incompressible flow problems, from microfluidics to viscous laminar and turbulent flows. The Proper Generalized Decomposition (PGD) will be used because it provides separated solutions, explicitly depending on the parameters of interest for the problem. The performance of a priori PGD and sampling-based a posteriori PGD is compared in terms of accuracy and computational cost for the simulation of Stokes flows in geometrically parameterized domains. This problem is particularly challenging as the geometric parameters affect both the solution manifold and the computational spatial domain. Moreover, in order to make the a priori PGD strategy appealing for industrial applications, a non-intrusive approach exploiting OpenFOAM native solver for incompressible flows is devised for viscous laminar and turbulent Navier-Stokes equations coupled with the Spalart-Allmaras model.
Deep Autoencoders Enhanced Manifold Learning for Digital Twin Application to Musculoskeletal Systems
J. S. Chen
William Prager Chair Professor, Department of Structural Engineering & Center for Extreme Events Research, University of California, San Diego, USA
The goal of this research is to develop a two-scale Digital Twin which integrates cellular scale musculoskeletal (MSK) models with structural scale system dynamics model for simulating human behavior under different environments, conditions, and constraints. The cellular scale models combine the image based physical models augmented with data-driven computing and learning algorithms for simulating muscle mechanics. Under this framework, the data-driven modeling is a hybrid approach that integrates universal physical laws with sensor data directly to circumvent the necessity of using phenomenological constitutive models. A robust data-driven simulation approach based on manifold learning based locally convex data-driven (LCDD) computing, is formulated under the image based RKPM framework. 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. An autoencoder is introduced to extract a low-dimensional representation (embedding) of data and addresses the “dimensionality curse” emerging from other conventional manifold learning-based methods. The data embeddings learned by the encoders provide enhanced noise filtering and extrapolation generalization. A local convexity-preserving scheme based on Shepard interpolation is introduced for the data-driven local solution to enhance numerical stability.
The cellular scale models are upscaled with the reduced order approach for coupling with the component and whole-body system dynamics models. The system dynamics models are calibrated with the motion tracking data by solving an optimization problem. This framework is formulated by enhancing Deep Neural Networks (DNNs) with physics-based constraints such as residuals of the governing equations. Adding the physics-based residual as a regularization term to the loss function of DNNs allows for a robust system identification procedure. The approach is further enhanced with modern machine learning architectures to yield a computationally efficient framework for system parameters and function identification. The future work in integrating various data streams of the subject including motion capture data (position, velocity, and acceleration) and wearable sensor data (kinetic and kinematic data of the muscle groups) for a better solution accuracy and connecting the system identification of the multi-body dynamics of the MSK DT to the patient specific muscle mechanical properties, is also highlighted.