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We propose a height-field-based real-time simulation method for sand and water mixtures. Inspired by the shallow-water assumption, our approach extends the governing equations to handle two-phase flows of sand and water using height fields. Our depth-integrated governing equations can model the elastoplastic behavior of sand, as well as sand-water-mixing phenomena such as friction, diffusion, saturation, and momentum exchange. We further propose an operator-splitting time integrator that is both GPU-friendly and stable under moderate time step sizes. We have evaluated our method on a set of benchmark scenarios involving large bodies of heterogeneous materials, where our GPU-based algorithm runs at real-time frame rates. Our method achieves a desirable trade-off between fidelity and performance, bringing an unprecedentedly immersive experience for real-time applications. 

We present a generalized constitutive model for versatile physics simulation of inviscid fluids, Newtonian viscosity, hyperelasticity, viscoplasticity, elastoplasticity, and other physical effects that arise due to a mixture of these behaviors. The key ideas behind our formulation are the design of a generalized Kirchhoff stress tensor that can describe hyperelasticity, Newtonian viscosity and inviscid fluids, and the use of pre-projection and post-correction rules for simulating material behaviors that involve plasticity, including elastoplasticity and viscoplasticity. We show how our generalized Kirchhoff stress tensor can be coupled together into a generalized constitutive model that allows the simulation of diverse material behaviors by only changing parameter values. We present several side-by-side comparisons with physics simulations for specific constitutive models to show that our generalized model produces visually similar results. More notably, our formulation allows for inverse learning of unknown material properties directly from data using differentiable physics simulations. We present several 3D simulations to highlight the robustness of our method, even with multiple different materials. To the best of our knowledge, our approach is the first to recover the knowledge of unknown material properties without making explicit assumptions about the data.

 

We present an end-to-end method for capturing the dynamics of 3D human characters and translating them for synthesizing new, visually-realistic motion sequences. Conventional methods employ sophisticated, but generic, control approaches for driving the joints of articulated characters, paying little attention to the distinct dynamics of human joint movements. In contrast, our approach attempts to synthesize human-like joint movements by exploiting a biologically-plausible, compact network of spiking neurons that drive joint control in primates and rodents. We adapt the controller architecture by introducing learnable components and propose an evolutionary algorithm for training the spiking neural network architectures and capturing diverse joint dynamics. Our method requires only a few samples for capturing the dynamic properties of a joint's motion and exploits the biologically-inspired, trained controller for its reconstruction. More importantly, it can transfer the captured dynamics to new visually-plausible motion sequences. To enable user-dependent tailoring of the resulting motion sequences, we develop an interactive framework that allows for editing and real-time visualization of the controlled 3D character. We also demonstrate the applicability of our method to real human motion capture data by learning the hand joint dynamics from a gesture dataset and using our framework to reconstruct the gestures with our 3D animated character. The compact architecture of our joint controller emerging from its biologically-realistic design, and the inherent capacity of our evolutionary learning algorithm for parallelization, suggest that our approach could provide an efficient and scalable alternative for synthesizing 3D character animations with diverse and visually-realistic motion dynamics.

 

This paper proposes fast polynomial evaluation methods for correctly rounded elementary functions generated using our RLibm approach. The resulting functions produce correct results for all inputs with multiple representations and rounding modes. Given an oracle, the RLibm approach approximates the correctly rounded result rather than the real value of an elementary function. A key observation is that there is an interval of real values around the correctly rounded result such that any real value in it rounds to the correct result. This interval is the maximum freedom available to RLibm’s polynomial generation procedure. Subsequently, the problem of generating correctly rounded elementary functions using these intervals can be structured as a linear programming problem. Our prior work on the RLibm approach uses Horner’s method for polynomial evaluation. This paper explores polynomial evaluation techniques such as Knuth’s coefficient adaptation procedure, parallel execution of operations using Estrin’s procedure, and the use of fused multiply-add operations in the context of the RLibm approach. If we take the polynomial generated by the RLibm approach and subsequently perform polynomial evaluation optimizations, it results in incorrect results due to rounding errors during polynomial evaluation. Hence, we propose to integrate the fast polynomial evaluation procedure in the RLibm’s polynomial generation process. Our new polynomial evaluation procedure that combines parallel execution with fused multiply-add operations outperforms the Horner’s method used by RLibm’s correctly rounded functions. We show the resulting polynomials for 32-bit float are not only correct but also faster than prior functions in RLibm by 24% 

This study presents a new method for modeling the interaction between compressible flow, shock waves, and deformable structures, emphasizing destructive dynamics. Extending advances in time-splitting compressible flow and the Material Point Methods (MPM), we develop a hybrid Eulerian and Lagrangian/Eulerian scheme for monolithic flow-structure interactions. We adopt the second-order WENO scheme to advance the continuity equation. To stably resolve deforming boundaries with sub-cell particles, we propose a blending treatment of reflective and passable boundary conditions inspired by the theory of porous media. The strongly coupled velocity-pressure system is discretized with a new mixed-order finite element formulation employing B-spline shape functions. Shock wave propagation, temperature/density-induced buoyancy effects, and topology changes in solids are unitedly captured. 

This paper presents a novel method for generating a single polynomial approximation that produces correctly rounded results for all inputs of an elementary function for multiple representations. The generated polynomial approximation has the nice property that the first few lower degree terms produce correctly rounded results for specific representations of smaller bitwidths, which we call progressive performance. To generate such progressive polynomial approximations, we approximate the correctly rounded result and formulate the computation of correctly rounded polynomial approximations as a linear program similar to our prior work on the RLIBM project. To enable the use of resulting polynomial approximations in mainstream libraries, we want to avoid piecewise polynomials with large lookup tables. We observe that the problem of computing polynomial approximations for elementary functions is a linear programming problem in low dimensions, i.e., with a small number of unknowns. We design a fast randomized algorithm for computing polynomial approximations with progressive performance. Our method produces correct and fast polynomials that require a small amount of storage. A few polynomial approximations from our prototype have already been incorporated into LLVM’s math library. 

Tensegrity robots, composed of rigid rods and flexible cables, are difficult to accurately model and control given the presence of complex dynamics and high number of DoFs. Differentiable physics engines have been recently proposed as a data-driven approach for model identification of such complex robotic systems. These engines are often executed at a high-frequency to achieve accurate simulation. Ground truth trajectories for training differentiable engines, however, are not typically available at such high frequencies due to limitations of real-world sensors. The present work focuses on this frequency mismatch, which impacts the modeling accuracy. We proposed a recurrent structure for a differentiable physics engine of tensegrity robots, which can be trained effectively even with low-frequency trajectories. To train this new recurrent engine in a robust way, this work introduces relative to prior work: (i) a new implicit integration scheme, (ii) a progressive training pipeline, and (iii) a differentiable collision checker. A model of NASA's icosahedron SUPERballBot on MuJoCo is used as the ground truth system to collect training data. Simulated experiments show that once the recurrent differentiable engine has been trained given the low-frequency trajectories from MuJoCo, it is able to match the behavior of MuJoCo's system. The criterion for success is whether a locomotion strategy learned using the differentiable engine can be transferred back to the ground-truth system and result in a similar motion. Notably, the amount of ground truth data needed to train the differentiable engine, such that the policy is transferable to the ground truth system, is 1% of the data needed to train the policy directly on the ground-truth system.