Fluid Simulation on Neural Flow Maps

We introduce Neural Flow Maps, a novel simulation method bridging the emerging paradigm of implicit neural representations with fluid simulation based on the theory of flow maps, to achieve state-of-the-art simulation of inviscid fluid phenomena. We devise a novel hybrid neural field representation, Spatially Sparse Neural Fields (SSNF), which fuses small neural networks with a pyramid of overlapping, multi-resolution, and spatially sparse grids, to compactly represent long-term spatiotemporal velocity fields at high accuracy. With this neural velocity buffer in hand, we compute long-term, bidirectional flow maps and their Jacobians in a mechanistically symmetric manner, to facilitate drastic accuracy improvement over existing solutions. These long-range, bidirectional flow maps enable high advection accuracy with low dissipation, which in turn facilitates high-fidelity incompressible flow simulations that manifest intricate vortical structures. We demonstrate the efficacy of our neural fluid simulation in a variety of challenging simulation scenarios, including leapfrogging vortices, colliding vortices, vortex reconnections, as well as vortex generation from moving obstacles and density differences. Our examples show increased performance over existing methods in terms of energy conservation, visual complexity, adherence to experimental observations, and preservation of detailed vortical structures.

Inferring Hybrid Neural Fluid Fields from Videos

We study recovering fluid density and velocity from sparse multiview videos. Existing neural dynamic reconstruction methods predominantly rely on optical flows; therefore, they cannot accurately estimate the density and uncover the underlying velocity due to the inherent visual ambiguities of fluid velocity, as fluids are often shapeless and lack stable visual features. The challenge is further pronounced by the turbulent nature of fluid flows, which calls for properly designed fluid velocity representations. To address these challenges, we propose hybrid neural fluid fields (HyFluid), a neural approach to jointly infer fluid density and velocity fields. Specifically, to deal with visual ambiguities of fluid velocity, we introduce a set of physics-based losses that enforce inferring a physically plausible velocity field, which is divergence-free and drives the transport of density. To deal with the turbulent nature of fluid velocity, we design a hybrid neural velocity representation that includes a base neural velocity field that captures most irrotational energy and a vortex particle-based velocity that models residual turbulent velocity. We show that our method enables recovering vortical flow details. Our approach opens up possibilities for various learning and reconstruction applications centered around 3D incompressible flow, including fluid re-simulation and editing, future prediction, and neural dynamic scene composition. Project website: https://kovenyu.com/HyFluid/

Skywork: A More Open Bilingual Foundation Model

In this technical report, we present Skywork-13B, a family of large language models (LLMs) trained on a corpus of over 3.2 trillion tokens drawn from both English and Chinese texts. This bilingual foundation model is the most extensively trained and openly published LLMs of comparable size to date. We introduce a two-stage training methodology using a segmented corpus, targeting general purpose training and then domain-specific enhancement training, respectively. We show that our model not only excels on popular benchmarks, but also achieves \emph{state of the art} performance in Chinese language modeling on diverse domains. Furthermore, we propose a novel leakage detection method, demonstrating that test data contamination is a pressing issue warranting further investigation by the LLM community. To spur future research, we release Skywork-13B along with checkpoints obtained during intermediate stages of the training process. We are also releasing part of our SkyPile corpus, a collection of over 150 billion tokens of web text, which is the largest high quality open Chinese pre-training corpus to date. We hope Skywork-13B and our open corpus will serve as a valuable open-source resource to democratize access to high-quality LLMs.

SkyMath: Technical Report

Large language models (LLMs) have shown great potential to solve varieties of natural language processing (NLP) tasks, including mathematical reasoning. In this work, we present SkyMath, a large language model for mathematics with 13 billion parameters. By applying self-compare fine-tuning, we have enhanced mathematical reasoning abilities of Skywork-13B-Base remarkably. On GSM8K, SkyMath outperforms all known open-source models of similar size and has established a new SOTA performance.

Reinforced Potential Field for Multi-Robot Motion Planning in Cluttered Environments

Motion planning is challenging for multiple robots in cluttered environments without communication, especially in view of real-time efficiency, motion safety, distributed computation, and trajectory optimality, etc. In this paper, a reinforced potential field method is developed for distributed multi-robot motion planning, which is a synthesized design of reinforcement learning and artificial potential fields. An observation embedding with a self-attention mechanism is presented to model the robot-robot and robot-environment interactions. A soft wall-following rule is developed to improve the trajectory smoothness. Our method belongs to reactive planning, but environment properties are implicitly encoded. The total amount of robots in our method can be scaled up to any number. The performance improvement over a vanilla APF and RL method has been demonstrated via numerical simulations. Experiments are also performed using quadrotors to further illustrate the competence of our method.

Motion Planning for Aerial Pick-and-Place based on Geometric Feasibility Constraints

This paper studies the motion planning problem of the pick-and-place of an aerial manipulator that consists of a quadcopter flying base and a Delta arm. We propose a novel partially decoupled motion planning framework to solve this problem. Compared to the state-of-the-art approaches, the proposed one has two novel features. First, it does not suffer from increased computation in high-dimensional configuration spaces. That is because it calculates the trajectories of the quadcopter base and the end-effector separately in the Cartesian space based on proposed geometric feasibility constraints. The geometric feasibility constraints can ensure the resulting trajectories satisfy the aerial manipulator's geometry. Second, collision avoidance for the Delta arm is achieved through an iterative approach based on a pinhole mapping method, so that the feasible trajectory can be found in an efficient manner. The proposed approach is verified by three experiments on a real aerial manipulation platform. The experimental results show the effectiveness of the proposed method for the aerial pick-and-place task.

Uncertainty Estimation for Deep Learning Image Reconstruction using a Local Lipschitz Metric

The use of deep learning approaches for image reconstruction is of contemporary interest in radiology, especially for approaches that solve inverse problems associated with imaging. In deployment, these models may be exposed to input distributions that are widely shifted from training data, due in part to data biases or drifts. We propose a metric based on local Lipschitz determined from a single trained model that can be used to estimate the model uncertainty for image reconstructions. We demonstrate a monotonic relationship between the local Lipschitz value and Mean Absolute Error and show that this method can be used to provide a threshold that determines whether a given DL reconstruction approach was well suited to the task. Our uncertainty estimation method can be used to identify out-of-distribution test samples, relate information regarding epistemic uncertainties, and guide proper data augmentation. Quantifying uncertainty of learned reconstruction approaches is especially pertinent to the medical domain where reconstructed images must remain diagnostically accurate.

Learning Neural Duplex Radiance Fields for Real-Time View Synthesis

Neural radiance fields (NeRFs) enable novel view synthesis with unprecedented visual quality. However, to render photorealistic images, NeRFs require hundreds of deep multilayer perceptron (MLP) evaluations - for each pixel. This is prohibitively expensive and makes real-time rendering infeasible, even on powerful modern GPUs. In this paper, we propose a novel approach to distill and bake NeRFs into highly efficient mesh-based neural representations that are fully compatible with the massively parallel graphics rendering pipeline. We represent scenes as neural radiance features encoded on a two-layer duplex mesh, which effectively overcomes the inherent inaccuracies in 3D surface reconstruction by learning the aggregated radiance information from a reliable interval of ray-surface intersections. To exploit local geometric relationships of nearby pixels, we leverage screen-space convolutions instead of the MLPs used in NeRFs to achieve high-quality appearance. Finally, the performance of the whole framework is further boosted by a novel multi-view distillation optimization strategy. We demonstrate the effectiveness and superiority of our approach via extensive experiments on a range of standard datasets.

Neural Partial Differential Equations with Functional Convolution

We present a lightweighted neural PDE representation to discover the hidden structure and predict the solution of different nonlinear PDEs. Our key idea is to leverage the prior of ``translational similarity'' of numerical PDE differential operators to drastically reduce the scale of learning model and training data. We implemented three central network components, including a neural functional convolution operator, a Picard forward iterative procedure, and an adjoint backward gradient calculator. Our novel paradigm fully leverages the multifaceted priors that stem from the sparse and smooth nature of the physical PDE solution manifold and the various mature numerical techniques such as adjoint solver, linearization, and iterative procedure to accelerate the computation. We demonstrate the efficacy of our method by robustly discovering the model and accurately predicting the solutions of various types of PDEs with small-scale networks and training sets. We highlight that all the PDE examples we showed were trained with up to 8 data samples and within 325 network parameters.

FluidLab: A Differentiable Environment for Benchmarking Complex Fluid Manipulation

Humans manipulate various kinds of fluids in their everyday life: creating latte art, scooping floating objects from water, rolling an ice cream cone, etc. Using robots to augment or replace human labors in these daily settings remain as a challenging task due to the multifaceted complexities of fluids. Previous research in robotic fluid manipulation mostly consider fluids governed by an ideal, Newtonian model in simple task settings (e.g., pouring). However, the vast majority of real-world fluid systems manifest their complexities in terms of the fluid's complex material behaviors and multi-component interactions, both of which were well beyond the scope of the current literature. To evaluate robot learning algorithms on understanding and interacting with such complex fluid systems, a comprehensive virtual platform with versatile simulation capabilities and well-established tasks is needed. In this work, we introduce FluidLab, a simulation environment with a diverse set of manipulation tasks involving complex fluid dynamics. These tasks address interactions between solid and fluid as well as among multiple fluids. At the heart of our platform is a fully differentiable physics simulator, FluidEngine, providing GPU-accelerated simulations and gradient calculations for various material types and their couplings. We identify several challenges for fluid manipulation learning by evaluating a set of reinforcement learning and trajectory optimization methods on our platform. To address these challenges, we propose several domain-specific optimization schemes coupled with differentiable physics, which are empirically shown to be effective in tackling optimization problems featured by fluid system's non-convex and non-smooth properties. Furthermore, we demonstrate reasonable sim-to-real transfer by deploying optimized trajectories in real-world settings.