We present a neural network-based simulation super-resolution framework that can efficiently and realistically enhance a facial performance produced by a low-cost, real-time physics-based simulation to a level of detail that closely approximates that of a reference-quality off-line simulator with much higher resolution (27× element count in our examples) and accurate physical modeling. Our approach is rooted in our ability to construct a training set of paired frames, from the low- and high-resolution simulators respectively, that are in semantic correspondence with each other. We use face animation as an exemplar of such a simulation domain, where creating this semantic congruence is achieved by simply dialing in the same muscle actuation controls and skeletal pose in the two simulators. Our proposed neural network super-resolution framework generalizes from this training set to unseen expressions, compensates for modeling discrepancies between the two simulations due to limited resolution or cost-cutting approximations in the real-time variant, and does not require any semantic descriptors or parameters to be provided as input, other than the result of the real-time simulation. We evaluate the efficacy of our pipeline on a variety of expressive performances and provide comparisons and ablation experiments for plausible variations and alternatives to our proposed scheme. Our code is available at https://github.com/hjoonpark/3d-sim-super- res.git.

We present f VDB, a novel GPU-optimized framework for deep learning on large-scale 3D data. f VDB provides a complete set of differentiable primitives to build deep learning architectures for common tasks in 3D learning such as convolution, pooling, attention, ray-tracing, meshing, etc. f VDB simultaneously provides a much larger feature set (primitives and operators) than established frameworks with no loss in efficiency: our operators match or exceed the performance of other frameworks with narrower scope. Furthermore, f VDB can process datasets with much larger footprint and spatial resolution than prior works, while providing a competitive memory footprint on small inputs. To achieve this combination of versatility and performance, f VDB relies on a single novel VDB index grid acceleration structure paired with several key innovations including GPU accelerated sparse grid construction, convolution using tensorcores, fast ray tracing kernels using a Hierarchical Digital Differential Analyzer algorithm (HDDA), and jagged tensors. Our framework is fully integrated with PyTorch enabling interoperability with existing pipelines, and we demonstrate its effectiveness on a number of representative tasks such as large-scale point-cloud segmentation, high resolution 3D generative modeling, unbounded scale Neural Radiance Fields, and large-scale point cloud reconstruction.

When considering sparse motion capture marker data, one typically struggles to balance its overfitting via a high dimensional blendshape system versus underfitting caused by smoothness constraints. With the current trend towards using more and more data, our aim is not to fit the motion capture markers with a parameterized (blendshape) model or to smoothly interpolate a surface through the marker positions, but rather to find an instance in the high resolution dataset that contains local geometry to fit each marker. Just as is true for typical machine learning applications, this approach benefits from a plethora of data, and thus we also consider augmenting the dataset via specially designed physical simulations that target the high resolution dataset such that the simulation output lies on the same so-called manifold as the data targeted.

Muscle-based systems have the potential to provide both anatomical accuracy and semantic interpretability as compared to blendshape models; however, a lack of expressivity and differentiability has limited their impact. Thus, we propose modifying a recently developed rather expressive muscle-based system in order to make it fully-differentiable; in fact, our proposed modifications allow this physically robust and anatomically accurate muscle model to conveniently be driven by an underlying blendshape basis. Our formulation is intuitive, natural, as well as monolithically and fully coupled such that one can differentiate the model from end to end, which makes it viable for both optimization and learning-based approaches for a variety of applications. We illustrate this with a number of examples including both shape matching of three-dimensional geometry as as well as the automatic determination of a three-dimensional facial pose from a single two-dimensional RGB image without using markers or depth information.

Many visually interesting natural phenomena are characterized by thin liquid sheets, long filaments, and droplets. We present a new Lagrangian-based numerical method to simulate these codimensional surface tension driven phenomena using non-manifold simplicial complexes. Tetrahedra, triangles, segments, and points are used to model the fluid volume, thin films, filaments, and droplets, respectively. We present a new method for enforcing fluid incompressibility on simplicial complexes along with a physically-guided meshing algorithm to provide temporally consistent information for interparticle forces. Our method naturally allows for transitions between codimensions, either from tetrahedra to triangles to segments to points or vice versa, regardless of the simulation resolution. We demonstrate the efficacy of this method by simulating various natural phenomena that are characterized by thin fluid sheets, filaments, and surface tension effects.

We present an efficient grid structure that extends a uniform grid to create a significantly larger far-field grid by dynamically extending the cells surrounding a fine uniform grid while still maintaining fine resolution about the regions of interest. The far-field grid preserves almost every computational advantage of uniform grids including cache coherency, regular subdivisions for parallelization, simple data layout, the existence of efficient numerical discretizations and algorithms for solving partial differential equations, etc. This allows fluid simulations to cover large domains that are often infeasible to enclose with sufficient resolution using a uniform grid, while still effectively capturing fine scale details in regions of interest using dynamic adaptivity.