Many dynamical systems -- from robots interacting with their surroundings to large-scale multiphysics systems -- involve a number of interacting subsystems. Toward the objective of learning composite models of such systems from data, we present i) a framework for compositional neural networks, ii) algorithms to train these models, iii) a method to compose the learned models, iv) theoretical results that bound the error of the resulting composite models, and v) a method to learn the composition itself, when it is not known a prior. The end result is a modular approach to learning: neural network submodels are trained on trajectory data generated by relatively simple subsystems, and the dynamics of more complex composite systems are then predicted without requiring additional data generated by the composite systems themselves. We achieve this compositionality by representing the system of interest, as well as each of its subsystems, as a port-Hamiltonian neural network (PHNN) -- a class of neural ordinary differential equations that uses the port-Hamiltonian systems formulation as inductive bias. We compose collections of PHNNs by using the system's physics-informed interconnection structure, which may be known a priori, or may itself be learned from data. We demonstrate the novel capabilities of the proposed framework through numerical examples involving interacting spring-mass-damper systems. Models of these systems, which include nonlinear energy dissipation and control inputs, are learned independently. Accurate compositions are learned using an amount of training data that is negligible in comparison with that required to train a new model from scratch. Finally, we observe that the composite PHNNs enjoy properties of port-Hamiltonian systems, such as cyclo-passivity -- a property that is useful for control purposes.
翻译:许多动态系统 -- -- 从机器人与其周围环境互动到大型多物理学系统 -- -- 涉及许多互动子系统。为了从数据中学习这些系统的复合模型,我们提出(一) 合成神经网络的框架,(二) 培训这些模型的算法,(三) 构建所学模型的方法,(四) 将由此产生的合成模型的错误捆绑起来的理论结果,(五) 学习构成本身的方法,而在此之前还不知道这一点。最终的结果是学习的模块化方法:神经网络子模型接受相对简单的子系统生成的轨迹数据培训,然后预测更复杂的复合系统的动态,而不需要综合系统本身生成的额外数据。我们通过代表兴趣系统及其每个子系统来实现这种构成性,作为港口-汉堡神经网络(PHNNN)的错误,这是使用港口-汉堡系统配置的普通差异方程式,我们通过使用系统内部系统独立生成的轨迹数据进行收集,而我们所了解的轨迹的轨迹,我们通过智能的机能系统来展示一个虚拟的智能数据结构。我们所了解的智能的网络,可以通过智能化的机变的机变的机变数据结构,我们所了解的机变的机变的机变数据结构,可以显示的机变数据结构,可以展示一个智能数据结构, 。