Despite existing 3D cloth simulators producing realistic results, they predominantly operate on discrete surface representations (e.g. points and meshes) with a fixed spatial resolution, which often leads to large memory consumption and resolution-dependent simulations. Moreover, back-propagating gradients through the existing solvers is difficult and they hence cannot be easily integrated into modern neural architectures. In response, this paper re-thinks physically plausible cloth simulation: We propose NeuralClothSim, i.e., a new quasistatic cloth simulator using thin shells, in which surface deformation is encoded in neural network weights in form of a neural field. Our memory-efficient solver operates on a new continuous coordinate-based surface representation called neural deformation fields (NDFs); it supervises NDF equilibria with the laws of the non-linear Kirchhoff-Love shell theory with a non-linear anisotropic material model. NDFs are adaptive: They 1) allocate their capacity to the deformation details and 2) allow surface state queries at arbitrary spatial resolutions without re-training. We show how to train NeuralClothSim while imposing hard boundary conditions and demonstrate multiple applications, such as material interpolation and simulation editing. The experimental results highlight the effectiveness of our continuous neural formulation.

Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) by enforcing outputs and gradients of deep models to satisfy target equations. Due to the limitation of numerical computation, PINNs are conventionally optimized on finite selected points. However, since PDEs are usually defined on continuous domains, solely optimizing models on scattered points may be insufficient to obtain an accurate solution for the whole domain. To mitigate this inherent deficiency of the default scatter-point optimization, this paper proposes and theoretically studies a new training paradigm as region optimization. Concretely, we propose to extend the optimization process of PINNs from isolated points to their continuous neighborhood regions, which can theoretically decrease the generalization error, especially for hidden high-order constraints of PDEs. A practical training algorithm, Region Optimized PINN (RoPINN), is seamlessly derived from this new paradigm, which is implemented by a straightforward but effective Monte Carlo sampling method. By calibrating the sampling process into trust regions, RoPINN finely balances optimization and generalization error. Experimentally, RoPINN consistently boosts the performance of diverse PINNs on a wide range of PDEs without extra backpropagation or gradient calculation. Code is available at this repository: https://github.com/thuml/RoPINN.

Classical Hamiltonian mechanics has been widely used in machine learning in the form of Hamiltonian Monte Carlo for applications with predetermined force fields. In this paper, we explore the potential of deliberately designing force fields for Hamiltonian systems, introducing Hamiltonian velocity predictors (HVPs) as a core tool for constructing energy-based and generative models. We present two innovations: Hamiltonian Score Matching (HSM), which utilizes score functions to augment data by simulating Hamiltonian trajectories, and Hamiltonian Generative Flows (HGFs), a novel generative model that encompasses diffusion models and OT-flow matching as HGFs with zero force fields. We showcase the extended design space of force fields by introducing Oscillation HGFs, a generative model inspired by harmonic oscillators. Our experiments demonstrate that HSM and HGFs rival leading score-matching and generative modeling techniques.

Agent-based models (ABMs) are proliferating as decision-making tools across policy areas in transportation, economics, and epidemiology. In these models, a central object of interest is the discrete origin-destination matrix which captures spatial interactions and agent trip counts between locations. Existing approaches resort to continuous approximations of this matrix and subsequent ad-hoc discretisations in order to perform ABM simulation and calibration. This impedes conditioning on partially observed summary statistics, fails to explore the multimodal matrix distribution over a discrete combinatorial support, and incurs discretisation errors. To address these challenges, we introduce a computationally efficient framework that scales linearly with the number of origin-destination pairs, operates directly on the discrete combinatorial space, and learns the agents' trip intensity through a neural differential equation that embeds spatial interactions. Our approach outperforms the prior art in terms of reconstruction error and ground truth matrix coverage, at a fraction of the computational cost. We demonstrate these benefits in two large-scale spatial mobility ABMs in Washington, DC and Cambridge, UK.

Recently, 3D Gaussian Splatting (3DGS) has emerged as a promising technique capable of real-time rendering with high-quality 3D reconstruction.

Object goal navigation requires an agent to navigate to a specified object in an unseen environment based on visual observations and user-specified goals. Human decision-making in navigation is sequential, planning a most likely sequence of actions toward the goal. However, existing ObjectNav methods, both end-to-end learning methods and modular methods, rely on single-step planning. They output the next action based on the current model input, which easily overlooks temporal consistency and leads to myopic planning.To this end, we aim to learn sequence planning for ObjectNav. Specifically, we propose trajectory diffusion to learn the distribution of trajectory sequences conditioned on the current observation and the goal. We utilize DDPM and automatically collected optimal trajectory segments to train the trajectory diffusion.Once the trajectory diffusion model is trained, it can generate a temporally coherent sequence of future trajectory for agent based on its current observations.Experimental results on the Gibson and MP3D datasets demonstrate that the generated trajectories effectively guide the agent, resulting in more accurate and efficient navigation.

The information processing in the brain and embodied agents form a sensory-action loop to interact with the world. An important step in the loop is motion planning which selects motor actions based on the current world state and task need. In goal-directed navigation, the brain chooses and generates motor actions to bring the current state into the goal state. It is unclear about the neural circuit mechanism of motor action selection, nor its underlying theory. The present study formulates the motion planning as a Lie group operator search problem, and uses the 1D rotation group as an example to provide insight into general operator search in neural circuits.

Reward Machines provide an automaton-inspired structure for specifying instructions, safety constraints, and other temporally extended reward-worthy behaviour. By exposing the underlying structure of a reward function, they enable the decomposition of an RL task, leading to impressive gains in sample efficiency. Although Reward Machines and similar formal specifications have a rich history of application towards sequential decision-making problems, prior frameworks have traditionally ignored ambiguity and uncertainty when interpreting the domain-specific vocabulary forming the building blocks of the reward function. Such uncertainty critically arises in many real-world settings due to factors like partial observability or noisy sensors. In this work, we explore the use of Reward Machines for Deep RL in noisy and uncertain environments. We characterize this problem as a POMDP and propose a suite of RL algorithms that exploit task structure under uncertain interpretation of the domain-specific vocabulary. Through theory and experiments, we expose pitfalls in naive approaches to this problem while simultaneously demonstrating how task structure can be successfully leveraged under noisy interpretations of the vocabulary.

For recent diffusion-based generative models, maintaining consistent content across a series of generated images, especially those containing subjects and complex details, presents a significant challenge. In this paper, we propose a simple but effective self-attention mechanism, termed Consistent Self-Attention, that boosts the consistency between the generated images. It can be used to augment pre-trained diffusion-based text-to-image models in a zero-shot manner. Based on the images with consistent content, we further show that our method can be extended to long range video generation by introducing a semantic space temporal motion prediction module, named Semantic Motion Predictor. It is trained to estimate the motion conditions between two provided images in the semantic spaces. This module converts the generated sequence of images into videos with smooth transitions and consistent subjects that are more stable than the modules based on latent spaces only, especially in the context of long video generation. By merging these two novel components, our framework, referred to as StoryDiffusion, can describe a text-based story with consistent images or videos encompassing a rich variety of contents. The proposed StoryDiffusion encompasses pioneering explorations in visual story generation with the presentation of images and videos, which we hope could inspire more research from the aspect of architectural modifications.

The swift advancement in Multimodal LLMs (MLLMs) also presents significant challenges for effective knowledge editing. Current methods, including intrinsic knowledge editing and external knowledge resorting, each possess strengths and weaknesses, struggling to balance the desired properties of reliability, generality, and locality when applied to MLLMs. In this paper, we propose \textbf{UniKE}, a novel multimodal editing method that establishes a unified perspective and paradigm for intrinsic knowledge editing and external knowledge resorting. Both types of knowledge are conceptualized as vectorized key-value memories, with the corresponding editing processes resembling the assimilation and accommodation phases of human cognition, conducted at the same semantic levels. Within such a unified framework, we further promote knowledge collaboration by disentangling the knowledge representations into the semantic and truthfulness spaces. Extensive experiments validate the effectiveness of our method, which ensures that the post-edit MLLM simultaneously maintains excellent reliability, generality, and locality.