Graph neural networks have been a powerful tool for mesh-based physical simulation. To efficiently model large-scale systems, existing methods mainly employ hierarchical graph structures to capture multi-scale node relations. However, these graph hierarchies are typically manually designed and fixed, limiting their ability to adapt to the evolving dynamics of complex physical systems. We propose EvoMesh, a fully differentiable framework that jointly learns graph hierarchies and physical dynamics, adaptively guided by physical inputs. EvoMesh introduces anisotropic message passing, which enables direction-specific aggregation of dynamic features between nodes within each hierarchy, while simultaneously learning node selection probabilities for the next hierarchical level based on physical context. This design creates more flexible message shortcuts and enhances the model’s capacity to capture long-range dependencies. Extensive experiments on five benchmark physical simulation datasets show that EvoMesh outperforms recent fixed-hierarchy message passing networks by large margins. The project page is available at https://hbell99.github.io/evo-mesh/.

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.

Conditional graphic layout generation, which generates realistic layouts according to user constraints, is a challenging task that has not been well-studied yet. First, there is limited discussion about how to handle diverse user constraints flexibly and uniformly. Second, to make the layouts conform to user constraints, existing work often sacrifices generation quality significantly. In this work, we propose LayoutFormer++ to tackle the above problems. First, to flexibly handle diverse constraints, we propose a constraint serialization scheme, which represents different user constraints as sequences of tokens with a predefined format. Then, we formulate conditional layout generation as a sequence-to-sequence transformation, and leverage encoder-decoder framework with Transformer as the basic architecture. Furthermore, to make the layout better meet user requirements without harming quality, we propose a decoding space restriction strategy. Specifically, we prune the predicted distribution by ignoring the options that definitely violate user constraints and likely result in low-quality layouts, and make the model samples from the restricted distribution. Experiments demonstrate that LayoutFormer++ outperforms existing approaches on all the tasks in terms of both better generation quality and less constraint violation.

Deep learning has shown great potential for modeling the physical dynamics of complex particle systems such as fluids. Existing approaches, however, require the supervision of consecutive particle properties, including positions and velocities. In this paper, we consider a partially observable scenario known as fluid dynamics grounding, that is, inferring the state transitions and interactions within the fluid particle systems from sequential visual observations of the fluid surface. We propose a differentiable two-stage network named NeuroFluid. Our approach consists of (i) a particle-driven neural renderer, which involves fluid physical properties into the volume rendering function, and (ii) a particle transition model optimized to reduce the differences between the rendered and the observed images. NeuroFluid provides the first solution to unsupervised learning of particle-based fluid dynamics by training these two models jointly. It is shown to reasonably estimate the underlying physics of fluids with different initial shapes, viscosity, and densities.

Though machine learning algorithms are able to achieve pattern recognition from the correlation between data and labels, the presence of spurious features in the data decreases the robustness of these learned relationships with respect to varied testing environments. This is known as out-of-distribution (OoD) generalization problem. Recently, invariant risk minimization (IRM) attempts to tackle this issue by penalizing predictions based on the unstable spurious features in the data collected from different environments. However, similar to domain adaptation or domain generalization, a prevalent non-trivial limitation in these works is that the environment information is assigned by human specialists, i.e. a priori, or determined heuristically. However, an inappropriate group partitioning can dramatically deteriorate the OoD generalization and this process is expensive and time-consuming. To deal with this issue, we propose a novel theoretically principled min-max framework to iteratively construct a worst-case splitting, i.e. creating the most challenging environment splittings for the backbone learning paradigm (e.g. IRM) to learn the robust feature representation. We also design a differentiable training strategy to facilitate the feasible gradient- based computation. Numerical experiments show that our algorithmic framework has achieved superior and stable performance in various datasets, such as Colored MNIST and Punctuated Stanford sentiment treebank (SST). Furthermore, we also find our algorithm to be robust even to a strong data poisoning attack. To the best of our knowledge, this is one of the first to adopt differentiable environment splitting method to enable stable predictions across environments without environment index information, which achieves the state-of-the-art performance on datasets with strong spurious correlation, such as Colored MNIST.