用流模型迁移外部条件下的分布，无需复杂架构或能量训练。
TRADE: Transfer of Distributions between External Conditions with Normalizing Flows
- 将分布迁移建模为边界值问题，利用梯度传播信息。
- 在分子模拟等任务中实现高精度参数依赖分布建模。
- 适合需要高效跨条件分布建模的研究者使用。
建模依赖外部控制参数的分布是分子模拟等应用中的常见问题，如温度影响分子构型。现有方法受限于严格模型结构或基于能量的训练，易产生不稳定性。本文提出TRADE，通过将学习过程定义为边界值问题克服这些限制。首先对特定条件进行独立同分布采样或反向KL训练，建立边界分布；随后利用未归一化密度对外部参数的梯度，将信息传播至其他条件。该方法类似物理信息神经网络原理，可无须强假设地高效学习参数依赖分布。实验表明，TRADE在贝叶斯推断、分子模拟和物理格点模型等多种场景中均取得优异表现。
原文摘要 · Abstract (English)
Modeling distributions that depend on external control parameters is a common scenario in diverse applications like molecular simulations, where system properties like temperature affect molecular configurations. Despite the relevance of these applications, existing solutions are unsatisfactory as they require severely restricted model architectures or rely on energy-based training, which is prone to instability. We introduce TRADE, which overcomes these limitations by formulating the learning process as a boundary value problem. By initially training the model for a specific condition using either i.i.d.~samples or backward KL training, we establish a boundary distribution. We then propagate this information across other conditions using the gradient of the unnormalized density with respect to the external parameter. This formulation, akin to the principles of physics-informed neural networks, allows us to efficiently learn parameter-dependent distributions without restrictive assumptions. Experimentally, we demonstrate that TRADE achieves excellent results in a wide range of applications, ranging from Bayesian inference and molecular simulations to physical lattice models.
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