Neural Force Field: Learning Generalized Physical Representation from a Few Examples

Physical reasoning is a remarkable human ability that enables rapid learning and generalization from limited experience. Current AI models, despite extensive training, still struggle to achieve similar generalization, especially in Out-of-distribution (OOD) settings. This limitation stems from their inability to abstract core physical principles from observations. A key challenge is developing representations that can efficiently learn and generalize physical dynamics from minimal data. Here we present Neural Force Field (NFF) a modeling framework built on Neural Ordinary Differential Equation (NODE) that learns interpretable force field representations which can be efficiently integrated through an Ordinary Differential Equation ( ODE) solver to predict object trajectories. Unlike existing approaches that rely on high-dimensional latent spaces, NFF captures fundamental physical concepts such as gravity, support, and collision in an interpretable manner. Experiments on two challenging physical reasoning tasks demonstrate that NFF, trained with only a few examples, achieves strong generalization to unseen scenarios. This physics-grounded representation enables efficient forward-backward planning and rapid adaptation through interactive refinement. Our work suggests that incorporating physics-inspired representations into learning systems can help bridge the gap between artificial and human physical reasoning capabilities.

I-PHYRE: Interactive Physical Reasoning

Current evaluation protocols predominantly assess physical reasoning in stationary scenes, creating a gap in evaluating agents' abilities to interact with dynamic events. While contemporary methods allow agents to modify initial scene configurations and observe consequences, they lack the capability to interact with events in real time. To address this, we introduce I-PHYRE, a framework that challenges agents to simultaneously exhibit intuitive physical reasoning, multi-step planning, and in-situ intervention. Here, intuitive physical reasoning refers to a quick, approximate understanding of physics to address complex problems; multi-step denotes the need for extensive sequence planning in I-PHYRE, considering each intervention can significantly alter subsequent choices; and in-situ implies the necessity for timely object manipulation within a scene, where minor timing deviations can result in task failure. We formulate four game splits to scrutinize agents' learning and generalization of essential principles of interactive physical reasoning, fostering learning through interaction with representative scenarios. Our exploration involves three planning strategies and examines several supervised and reinforcement agents' zero-shot generalization proficiency on I-PHYRE. The outcomes highlight a notable gap between existing learning algorithms and human performance, emphasizing the imperative for more research in enhancing agents with interactive physical reasoning capabilities. The environment and baselines will be made publicly available.

On the Learning Mechanisms in Physical Reasoning

Is dynamics prediction indispensable for physical reasoning? If so, what kind of roles do the dynamics prediction modules play during the physical reasoning process? Most studies focus on designing dynamics prediction networks and treating physical reasoning as a downstream task without investigating the questions above, taking for granted that the designed dynamics prediction would undoubtedly help the reasoning process. In this work, we take a closer look at this assumption, exploring this fundamental hypothesis by comparing two learning mechanisms: Learning from Dynamics (LfD) and Learning from Intuition (LfI). In the first experiment, we directly examine and compare these two mechanisms. Results show a surprising finding: Simple LfI is better than or on par with state-of-the-art LfD. This observation leads to the second experiment with Ground-truth Dynamics, the ideal case of LfD wherein dynamics are obtained directly from a simulator. Results show that dynamics, if directly given instead of approximated, would achieve much higher performance than LfI alone on physical reasoning; this essentially serves as the performance upper bound. Yet practically, LfD mechanism can only predict Approximate Dynamics using dynamics learning modules that mimic the physical laws, making the following downstream physical reasoning modules degenerate into the LfI paradigm; see the third experiment. We note that this issue is hard to mitigate, as dynamics prediction errors inevitably accumulate in the long horizon. Finally, in the fourth experiment, we note that LfI, the extremely simpler strategy when done right, is more effective in learning to solve physical reasoning problems. Taken together, the results on the challenging benchmark of PHYRE show that LfI is, if not better, as good as LfD for dynamics prediction. However, the potential improvement from LfD, though challenging, remains lucrative.