Fig. 1. Our convolutional neural network learns to generate highly detailed, and temporally coherent features based on a low-resolution field containing a single time-step of density and velocity data. We introduce a novel discriminator that ensures the synthesized details change smoothly over time.We propose a temporally coherent generative model addressing the superresolution problem for fluid flows. Our work represents a first approach to synthesize four-dimensional physics fields with neural networks. Based on a conditional generative adversarial network that is designed for the inference of three-dimensional volumetric data, our model generates consistent and detailed results by using a novel temporal discriminator, in addition to the commonly used spatial one. Our experiments show that the generator is able to infer more realistic high-resolution details by using additional physical quantities, such as low-resolution velocities or vorticities. Besides improvements in the training process and in the generated outputs, these inputs offer means for artistic control as well. We additionally employ a physics-aware data augmentation step, which is crucial to avoid overfitting and to reduce memory requirements. In this way, our network learns to generate advected quantities with highly detailed, realistic, and temporally coherent features. Our method works instantaneously, using only a single time-step of low-resolution fluid data. We demonstrate the abilities of our (*) Similar amount of contributions.

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High-fidelity reconstruction of dynamic fluids from sparse multiview RGB videos remains a formidable challenge, due to the complexity of the underlying physics as well as the severe occlusion and complex lighting in the captured data. Existing solutions either assume knowledge of obstacles and lighting, or only focus on simple fluid scenes without obstacles or complex lighting, and thus are unsuitable for real-world scenes with unknown lighting conditions or arbitrary obstacles. We present the first method to reconstruct dynamic fluid phenomena by leveraging the governing physics (ie, Navier -Stokes equations) in an end-to-end optimization from a mere set of sparse video frames without taking lighting conditions, geometry information, or boundary conditions as input. Our method provides a continuous spatio-temporal scene representation using neural networks as the ansatz of density and velocity solution functions for fluids as well as the radiance field for static objects. With a hybrid architecture that separates static and dynamic contents apart, fluid interactions with static obstacles are reconstructed for the first time without additional geometry input or human labeling. By augmenting time-varying neural radiance fields with physics-informed deep learning, our method benefits from the supervision of images and physical priors. Our progressively growing model with regularization further disentangles the density-color ambiguity in the radiance field, which allows for a more robust optimization from the given input of sparse views. A pretrained density-to-velocity fluid model is leveraged in addition as the data prior to avoid suboptimal velocity solutions which underestimate vorticity but trivially fulfill physical equations. Our method exhibits high-quality results with relaxed constraints and strong flexibility on a representative set of synthetic and real flow captures. Code and sample tests are at https://people.mpi-inf.mpg.de/~mchu/projects/PI-NeRF/.

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