用自监督学习从轨迹推断复杂系统的能量景观，精度超90%。
Predicting the Energy Landscape of Stochastic Dynamical System via Physics-informed Self-supervised Learning
- 通过自适应码本将状态映射到离散能级空间，结合图神经网络求解福克-普朗克方程。
- 能级估计相关系数达0.9以上，演化预测准确率比基线平均提升17.65%。
- 适合研究随机动力系统、生物分子运动与物理建模的科研人员。
能量景观在众多真实复杂系统中起关键作用。系统演化常被建模为粒子在能量驱动漂移与噪声扩散共同作用下沿景观移动，其中能量决定粒子长期运动趋势。由于获取真实能量值成本高或缺乏监督信号，估计系统能量景观一直是跨学科难题。本文提出一种物理信息自监督学习方法，仅从系统演化轨迹中推断能量景观。首先通过自适应码本将系统状态映射到离散景观空间，再显式地将能量引入图神经福克-普朗克方程，实现能量估计与演化预测的联合学习。跨多领域系统实验表明，所估能量与真实值相关系数超过0.9，演化预测精度较基线平均提升17.65%。代码已开源：github.com/tsinghua-fib-lab/PESLA。
原文摘要 · Abstract (English)
Energy landscapes play a crucial role in shaping dynamics of many real-world complex systems. System evolution is often modeled as particles moving on a landscape under the combined effect of energy-driven drift and noise-induced diffusion, where the energy governs the long-term motion of the particles. Estimating the energy landscape of a system has been a longstanding interdisciplinary challenge, hindered by the high operational costs or the difficulty of obtaining supervisory signals. Therefore, the question of how to infer the energy landscape in the absence of true energy values is critical. In this paper, we propose a physics-informed self-supervised learning method to learn the energy landscape from the evolution trajectories of the system. It first maps the system state from the observation space to a discrete landscape space by an adaptive codebook, and then explicitly integrates energy into the graph neural Fokker-Planck equation, enabling the joint learning of energy estimation and evolution prediction. Experimental results across interdisciplinary systems demonstrate that our estimated energy has a correlation coefficient above 0.9 with the ground truth, and evolution prediction accuracy exceeds the baseline by an average of 17.65\%. The code is available at github.com/tsinghua-fib-lab/PESLA.
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