All fields of science depend on mathematical models. One of the fundamental problems with using complex nonlinear models is that data-driven parameter estimation often fails because interactions between model parameters lead to multiple parameter sets fitting the data equally well. Here, we develop a new method to address this problem, FixFit, which compresses a given mathematical model's parameters into a latent representation unique to model outputs. We acquire this representation by training a neural network with a bottleneck layer on data pairs of model parameters and model outputs. The bottleneck layer nodes correspond to the unique latent parameters, and their dimensionality indicates the information content of the model. The trained neural network can be split at the bottleneck layer into an encoder to characterize the redundancies and a decoder to uniquely infer latent parameters from measurements. We demonstrate FixFit in two use cases drawn from classical physics and neuroscience.

翻译：所有科学领域都依赖于数学模型。使用复杂非线性模型的一个基本问题是，数据驱动的参数估计常常失败，因为模型参数间的相互作用会导致多组参数集同等程度地拟合数据。本文提出了一种解决该问题的新方法——FixFit，该方法通过将给定数学模型的参数压缩为模型输出唯一的潜在表示来达成目标。我们通过使用带瓶颈层的神经网络对模型参数和模型输出的数据对进行训练来获取这种表示。瓶颈层节点对应于唯一的潜在参数，其维度揭示了模型的信息含量。训练后的神经网络可在瓶颈层处拆分为编码器和解码器，前者用于表征冗余性，后者用于从测量数据中唯一推断潜在参数。我们通过古典物理学和神经科学领域的两个应用实例展示了FixFit的有效性。