Recent machine learning algorithms dedicated to solving semi-linear PDEs are improved by using different neural network architectures and different parameterizations. These algorithms are compared to a new one that solves a fixed point problem by using deep learning techniques. This new algorithm appears to be competitive in terms of accuracy with the best existing algorithms.
We introduce three new generative models for time series that are based on Euler discretization of Stochastic Differential Equations (SDEs) and Wasserstein metrics. Two of these methods rely on the adaptation of generative adversarial networks (GANs) to time series. The third algorithm, called Conditional Euler Generator (CEGEN), minimizes a dedicated distance between the transition probability distributions over all time steps. In the context of Itô processes, we provide theoretical guarantees that minimizing this criterion implies accurate estimations of the drift and volatility parameters. Empirically, CEGEN outperforms state-of-the-art and GANs on both marginal and temporal dynamic metrics. Besides, correlation structures are accurately identified in high dimension. When few real data points are available, we verify the effectiveness of CEGEN when combined with transfer learning methods on model-based simulations. Finally, we illustrate the robustness of our methods on various real-world data sets.
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