Figure 1: Comparison between Lagrangian (left) and Eulerian (right) perspectives.

Figure 1: Comparison between Lagrangian (left) and Eulerian (right) perspectives.

In recent years, VLMs have captured the imagination of the Artificial Intelligence(AI) community, demonstrating an impressive ability to interpret, reason about, and generate content that covers both text and image handling. From answering questions about visual scenes to engaging in multi-modal dialogue, models such as Flamingo [1], PaLI [25], and BLIP-2 [14] are redefining the frontier of vision intelligence. Y et, as these models are widening their application capabilities, a fundamental question emerges: can they truly reason, or are they sophisticated pattern matchers? To explore this question, we turn to the domain of physics--a field that serves as a universal benchmark for logical thoughts of a human being. Physics problems are an ideal testbed for VLMs, as they are multi-modal, combining textual descriptions, mathematical equations, and often clarifying diagrams. A model that can successfully solve these problems must not only understand language and images but also grasp the underlying relationships and principles that govern the physical realm. The challenge, uptil now, has been the lack of accessible tools for this kind of evaluation. Existing benchmarks for scientific reasoning, such as ARC [7] and ScienceQA [17], are often limited to basic text-only question sets, while those that incorporate visual elements, like MathVista [18], frequently depend on complex physics simulators that are computationally expensive for many researchers to deploy, thereby restricting reproducibility.

We train Fourier Neural Operator (FNO) surrogate models for Rayleigh-B\'enard Convection (RBC), a model for convection processes that occur in nature and industrial settings. We compare the prediction accuracy and model properties of FNO surrogates to two popular surrogates used in fluid dynamics: the Dynamic Mode Decomposition and the Linearly-Recurrent Autoencoder Network. We regard Direct Numerical Simulations (DNS) of the RBC equations as the ground truth on which the models are trained and evaluated in different settings. The FNO performs favorably when compared to the DMD and LRAN and its predictions are fast and highly accurate for this task. Additionally, we show its zero-shot super-resolution ability for the convection dynamics. The FNO model has a high potential to be used in downstream tasks such as flow control in RBC.

Fluid simulation is an important research topic in computer graphics (CG) and animation in video games. Traditional methods based on Navier-Stokes equations are computationally expensive. In this paper, we treat fluid motion as point cloud transformation and propose the first neural network method specifically designed for efficient and robust fluid simulation in complex environments. This model is also the deep learning model that is the first to be capable of stably modeling fluid particle dynamics in such complex scenarios. Our triangle feature fusion design achieves an optimal balance among fluid dynamics modeling, momentum conservation constraints, and global stability control. We conducted comprehensive experiments on datasets. Compared to existing neural network-based fluid simulation algorithms, we significantly enhanced accuracy while maintaining high computational speed. Compared to traditional SPH methods, our speed improved approximately 10 times. Furthermore, compared to traditional fluid simulation software such as Flow3D, our computation speed increased by more than 300 times.

We test the hypothesis that the microscopic temporal structure of near-field turbulence downstream of a sudden contraction contains geometry-identifiable information pertaining to the shape of the upstream obstruction. We measure a set of spatially sparse velocity time-series data downstream of differently-shaped orifices. We then train random forest multiclass classifier models on a vector of invariants derived from this time-series. We test the above hypothesis with 25 somewhat similar orifice shapes to push the model to its extreme limits. Remarkably, the algorithm was able to identify the orifice shape with 100% accuracy and 100% precision. This outcome is enabled by the uniqueness in the downstream temporal evolution of turbulence structures in the flow past orifices, combined with the random forests' ability to learn subtle yet discerning features in the turbulence microstructure. We are also able to explain the underlying flow physics that enables such classification by listing the invariant measures in the order of increasing information entropy. We show that the temporal autocorrelation coefficients of the time-series are most sensitive to orifice shape and are therefore informative. The ability to identify changes in system geometry without the need for physical disassembly offers tremendous potential for flow control and system identification. Furthermore, the proposed approach could potentially have significant applications in other unrelated fields as well, by deploying the core methodology of training random forest classifiers on vectors of invariant measures obtained from time-series data.

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.

Accurately predicting the future fluid is important to extensive areas, such as meteorology, oceanology and aerodynamics. However, since the fluid is usually observed from an Eulerian perspective, its active and intricate dynamics are seriously obscured and confounded in static grids, bringing horny challenges to the prediction. This paper introduces a new Lagrangian-guided paradigm to tackle the tanglesome fluid dynamics. Instead of solely predicting the future based on Eulerian observations, we propose the Eulerian-Lagrangian Dual Recurrent Network (EuLagNet), which captures multiscale fluid dynamics by tracking movements of adaptively sampled key particles on multiple scales and integrating dynamics information over time. Concretely, a EuLag Block is presented to communicate the learned Eulerian and Lagrangian features at each moment and scale, where the motion of tracked particles is inferred from Eulerian observations and their accumulated dynamics information is incorporated into Eulerian fields to guide future prediction. Tracking key particles not only provides a clear and interpretable clue for fluid dynamics but also makes our model free from modeling complex correlations among massive grids for better efficiency. Experimentally, EuLagNet excels in three challenging fluid prediction tasks, covering both 2D and 3D, simulated and real-world fluids.