DimOL: Dimensional Awareness as A New 'Dimension' in Operator Learning

In the realm of computational physics, an enduring topic is the numerical solutions to partial differential equations (PDEs). Recently, the attention of researchers has shifted towards Neural Operator methods, renowned for their capability to approximate ``operators'' -- mappings from functions to functions. Despite the universal approximation theorem within neural operators, ensuring error bounds often requires employing numerous Fourier layers. However, what about lightweight models? In response to this question, we introduce DimOL (Dimension-aware Operator Learning), drawing insights from dimensional analysis. To implement DimOL, we propose the ProdLayer, which can be seamlessly integrated into FNO-based and Transformer-based PDE solvers, enhancing their ability to handle sum-of-products structures inherent in many physical systems. Empirically, DimOL models achieve up to 48% performance gain within the PDE datasets. Furthermore, by analyzing Fourier components' weights, we can symbolically discern the physical significance of each term. This sheds light on the opaque nature of neural networks, unveiling underlying physical principles.

Open-World Reinforcement Learning over Long Short-Term Imagination

Training visual reinforcement learning agents in a high-dimensional open world presents significant challenges. While various model-based methods have improved sample efficiency by learning interactive world models, these agents tend to be "short-sighted", as they are typically trained on short snippets of imagined experiences. We argue that the primary obstacle in open-world decision-making is improving the efficiency of off-policy exploration across an extensive state space. In this paper, we present LS-Imagine, which extends the imagination horizon within a limited number of state transition steps, enabling the agent to explore behaviors that potentially lead to promising long-term feedback. The foundation of our approach is to build a long short-term world model. To achieve this, we simulate goal-conditioned jumpy state transitions and compute corresponding affordance maps by zooming in on specific areas within single images. This facilitates the integration of direct long-term values into behavior learning. Our method demonstrates significant improvements over state-of-the-art techniques in MineDojo.

Discovering Message Passing Hierarchies for Mesh-Based Physics Simulation

Graph neural networks have emerged as a powerful tool for large-scale mesh-based physics simulation. Existing approaches primarily employ hierarchical, multi-scale message passing to capture long-range dependencies within the graph. However, these graph hierarchies are typically fixed and manually designed, which do not adapt to the evolving dynamics present in complex physical systems. In this paper, we introduce a novel neural network named DHMP, which learns Dynamic Hierarchies for Message Passing networks through a differentiable node selection method. The key component is the anisotropic message passing mechanism, which operates at both intra-level and inter-level interactions. Unlike existing methods, it first supports directionally non-uniform aggregation of dynamic features between adjacent nodes within each graph hierarchy. Second, it determines node selection probabilities for the next hierarchy according to different physical contexts, thereby creating more flexible message shortcuts for learning remote node relations. Our experiments demonstrate the effectiveness of DHMP, achieving 22.7% improvement on average compared to recent fixed-hierarchy message passing networks across five classic physics simulation datasets.

Learning Augmentation Policies from A Model Zoo for Time Series Forecasting

Time series forecasting models typically rely on a fixed-size training set and treat all data uniformly, which may not effectively capture the specific patterns present in more challenging training samples. To address this issue, we introduce AutoTSAug, a learnable data augmentation method based on reinforcement learning. Our approach begins with an empirical analysis to determine which parts of the training data should be augmented. Specifically, we identify the so-called marginal samples by considering the prediction diversity across a set of pretrained forecasting models. Next, we propose using variational masked autoencoders as the augmentation model and applying the REINFORCE algorithm to transform the marginal samples into new data. The goal of this generative model is not only to mimic the distribution of real data but also to reduce the variance of prediction errors across the model zoo. By augmenting the marginal samples with a learnable policy, AutoTSAug substantially improves forecasting performance, advancing the prior art in this field with minimal additional computational cost.

Dynamic Scene Understanding through Object-Centric Voxelization and Neural Rendering

Learning object-centric representations from unsupervised videos is challenging. Unlike most previous approaches that focus on decomposing 2D images, we present a 3D generative model named DynaVol-S for dynamic scenes that enables object-centric learning within a differentiable volume rendering framework. The key idea is to perform object-centric voxelization to capture the 3D nature of the scene, which infers per-object occupancy probabilities at individual spatial locations. These voxel features evolve through a canonical-space deformation function and are optimized in an inverse rendering pipeline with a compositional NeRF. Additionally, our approach integrates 2D semantic features to create 3D semantic grids, representing the scene through multiple disentangled voxel grids. DynaVol-S significantly outperforms existing models in both novel view synthesis and unsupervised decomposition tasks for dynamic scenes. By jointly considering geometric structures and semantic features, it effectively addresses challenging real-world scenarios involving complex object interactions. Furthermore, once trained, the explicitly meaningful voxel features enable additional capabilities that 2D scene decomposition methods cannot achieve, such as novel scene generation through editing geometric shapes or manipulating the motion trajectories of objects.

Latent Intuitive Physics: Learning to Transfer Hidden Physics from A 3D Video

We introduce latent intuitive physics, a transfer learning framework for physics simulation that can infer hidden properties of fluids from a single 3D video and simulate the observed fluid in novel scenes. Our key insight is to use latent features drawn from a learnable prior distribution conditioned on the underlying particle states to capture the invisible and complex physical properties. To achieve this, we train a parametrized prior learner given visual observations to approximate the visual posterior of inverse graphics, and both the particle states and the visual posterior are obtained from a learned neural renderer. The converged prior learner is embedded in our probabilistic physics engine, allowing us to perform novel simulations on unseen geometries, boundaries, and dynamics without knowledge of the true physical parameters. We validate our model in three ways: (i) novel scene simulation with the learned visual-world physics, (ii) future prediction of the observed fluid dynamics, and (iii) supervised particle simulation. Our model demonstrates strong performance in all three tasks.

GS-Phong: Meta-Learned 3D Gaussians for Relightable Novel View Synthesis

Decoupling the illumination in 3D scenes is crucial for novel view synthesis and relighting. In this paper, we propose a novel method for representing a scene illuminated by a point light using a set of relightable 3D Gaussian points. Inspired by the Blinn-Phong model, our approach decomposes the scene into ambient, diffuse, and specular components, enabling the synthesis of realistic lighting effects. To facilitate the decomposition of geometric information independent of lighting conditions, we introduce a novel bilevel optimization-based meta-learning framework. The fundamental idea is to view the rendering tasks under various lighting positions as a multi-task learning problem, which our meta-learning approach effectively addresses by generalizing the learned Gaussian geometries not only across different viewpoints but also across diverse light positions. Experimental results demonstrate the effectiveness of our approach in terms of training efficiency and rendering quality compared to existing methods for free-viewpoint relighting.

Vid2Act: Activate Offline Videos for Visual RL

Pretraining RL models on offline video datasets is a promising way to improve their training efficiency in online tasks, but challenging due to the inherent mismatch in tasks, dynamics, and behaviors across domains. A recent model, APV, sidesteps the accompanied action records in offline datasets and instead focuses on pretraining a task-irrelevant, action-free world model within the source domains. We present Vid2Act, a model-based RL method that learns to transfer valuable action-conditioned dynamics and potentially useful action demonstrations from offline to online settings. The main idea is to use the world models not only as simulators for behavior learning but also as tools to measure the domain relevance for both dynamics representation transfer and policy transfer. Specifically, we train the world models to generate a set of time-varying task similarities using a domain-selective knowledge distillation loss. These similarities serve two purposes: (i) adaptively transferring the most useful source knowledge to facilitate dynamics learning, and (ii) learning to replay the most relevant source actions to guide the target policy. We demonstrate the advantages of Vid2Act over the action-free visual RL pretraining method in both Meta-World and DeepMind Control Suite.

Collaborative World Models: An Online-Offline Transfer RL Approach

Training visual reinforcement learning (RL) models in offline datasets is challenging due to overfitting issues in representation learning and overestimation problems in value function. In this paper, we propose a transfer learning method called Collaborative World Models (CoWorld) to improve the performance of visual RL under offline conditions. The core idea is to use an easy-to-interact, off-the-shelf simulator to train an auxiliary RL model as the online "test bed" for the offline policy learned in the target domain, which provides a flexible constraint for the value function -- Intuitively, we want to mitigate the overestimation problem of value functions outside the offline data distribution without impeding the exploration of actions with potential advantages. Specifically, CoWorld performs domain-collaborative representation learning to bridge the gap between online and offline hidden state distributions. Furthermore, it performs domain-collaborative behavior learning that enables the source RL agent to provide target-aware value estimation, allowing for effective offline policy regularization. Experiments show that CoWorld significantly outperforms existing methods in offline visual control tasks in DeepMind Control and Meta-World.

Object-Centric Voxelization of Dynamic Scenes via Inverse Neural Rendering

Understanding the compositional dynamics of the world in unsupervised 3D scenarios is challenging. Existing approaches either fail to make effective use of time cues or ignore the multi-view consistency of scene decomposition. In this paper, we propose DynaVol, an inverse neural rendering framework that provides a pilot study for learning time-varying volumetric representations for dynamic scenes with multiple entities (like objects). It has two main contributions. First, it maintains a time-dependent 3D grid, which dynamically and flexibly binds the spatial locations to different entities, thus encouraging the separation of information at a representational level. Second, our approach jointly learns grid-level local dynamics, object-level global dynamics, and the compositional neural radiance fields in an end-to-end architecture, thereby enhancing the spatiotemporal consistency of object-centric scene voxelization. We present a two-stage training scheme for DynaVol and validate its effectiveness on various benchmarks with multiple objects, diverse dynamics, and real-world shapes and textures. We present visualization at https://sites.google.com/view/dynavol-visual.