GAMES Webinar 2020 – 137期(仿真模拟专题) | Yin Yang(Clemson University), Hongyi Xu(Google Research)
【GAMES Webinar 2020-137期】(仿真模拟专题)
报告嘉宾1：Yin Yang(Clemson University)
报告题目：Accelerated Complex Finite Difference for Convenient Deformable Simulation
Numerical derivative is an essential computing task in many graphics research problems. The standard numerical routine is the finite difference method, which evaluates the target function multiple times with a small real-valued perturbation. The ratio between the change of the function value and the perturbation is then used to approximate the derivative of the target function. However, the round-off error inherited in the digit computer prevents us from employing an arbitrarily small perturbation. Therefore, real value finite difference is doomed for the computing problems that require a high-accuracy evaluation of derivative functions. In this paper, we show a new finite difference scheme that yields a highly accurate derivative approximation. The key strategy is to promote the original target function to be a complex one, and apply the perturbation to its imaginary domain. Doing so avoids the subtractive operation in the standard finite difference routine, which is mostly affected by the round-off error due to the loss of significant digits. As a result, one can use a very small perturbation and obtain a numerical derivative that is as accurate as the analytic derivative. We propose a collection of novel numerical techniques to accelerate this new complex-based finite difference scheme and multifold speedups are observed. This is achieved by carefully dropping unneeded high-order error terms, decoupling real and imaginary calculations, replacing costly functions based on the theory of equivalent infinitesimal, and isolating the propagation of the perturbation in composite relations. As a result, the accelerated numerical derivative is also as efficient as the analytic derivative. We demonstrate the accuracy, convenience, and efficiency of this new numerical routine in the context of solid simulation — one can easily deploy a robust simulator for any hyperelastic materials, including user-crafted ones to cater specific needs in different applications. The first- and second- order derivatives of the elastic energy (i.e. the internal force and the tangent stiffness matrix) can be accurately computed without knowing their closed-form formulation. Higher-order derivative of the energy can also be computed so that modal derivative bases are constructed to enable reduced real-time simulation. This method can be further generalized to handle tensor functions. Therefore, inverse simulation problems can be conveniently solved using gradient/Hessian based optimization procedures.
Dr. Yin Yang is an Associate Professor with School of Computing at Clemson. Before joining Clemson, he was a faculty member at the University of New Mexico, Albuquerque. Dr. Yang received Ph.D. degree of Computer Science from The University of Texas, Dallas in 2013 (he was the awardee of David Daniel Fellowship Prize). He was a Research Intern in Microsoft Research Asia in 2012. Dr. Yang received NSF CRII award and CAREER award.
报告嘉宾2：Hongyi Xu(Google Research)
报告题目：Physics-Aware Compliant Robotic Characters from Animation
Fueled by advances in digital fabrication technologies, there have seen a surge of research efforts aimed at bringing animated characters to the real world. In this talk, I will present our recent computation-driven approaches for creating elastic robotic characters from traditional animation rigs and motions, leveraging fast and accurate physically based simulations. Specifically, I first will present a computational technique for design of kinetic wire characters that takes as input a network of curves or a skeletal animation, then estimates a cable-driven, compliant wire structure which matches keyframes as closely as possible. To minimize displeasing artifacts that arise from structural vibrations on real-world fast-moving characters, we then develop an optimization-based, dynamics-aware motion retargeting system that adjusts the motor controls automatically, leveraging a differentiable dynamics simulator. Thanks to our computational design approaches, we have designed various robotics characters that present physical motion as closely as possible to the artistic intent.
Hongyi Xu is currently a research scientist in Google Research since Feb. 2019. Before that, he obtained his phd degree from University of Southern California in 2017 and his bachelor degree from Zhejiang University in 2012. During 2017-2019, he worked at Disney Research Zurich. He has worked on physically-based simulation/animation, computational fabrication and robotics, 3D human modeling and reconstruction, geometric modelling and haptics.
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