Probabilistic Forecasting with Stochastic Interpolants and Föllmer Processes

• URL: http://arxiv.org/abs/2403.13724v2
• Date: Tue, 27 Aug 2024 18:42:55 GMT
• Title: Probabilistic Forecasting with Stochastic Interpolants and Föllmer Processes
• Authors: Yifan Chen, Mark Goldstein, Mengjian Hua, Michael S. Albergo, Nicholas M. Boffi, Eric Vanden-Eijnden,
• Abstract summary: We propose a framework for probabilistic forecasting of dynamical systems based on generative modeling. We show that the drift and the diffusion coefficients of this SDE can be adjusted after training, and that a specific choice that minimizes the impact of the estimation error gives a F"ollmer process.
• Score: 18.344934424278048
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a framework for probabilistic forecasting of dynamical systems based on generative modeling. Given observations of the system state over time, we formulate the forecasting problem as sampling from the conditional distribution of the future system state given its current state. To this end, we leverage the framework of stochastic interpolants, which facilitates the construction of a generative model between an arbitrary base distribution and the target. We design a fictitious, non-physical stochastic dynamics that takes as initial condition the current system state and produces as output a sample from the target conditional distribution in finite time and without bias. This process therefore maps a point mass centered at the current state onto a probabilistic ensemble of forecasts. We prove that the drift coefficient entering the stochastic differential equation (SDE) achieving this task is non-singular, and that it can be learned efficiently by square loss regression over the time-series data. We show that the drift and the diffusion coefficients of this SDE can be adjusted after training, and that a specific choice that minimizes the impact of the estimation error gives a F\"ollmer process. We highlight the utility of our approach on several complex, high-dimensional forecasting problems, including stochastically forced Navier-Stokes and video prediction on the KTH and CLEVRER datasets.

Related papers

• ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equations [18.64802090861607]
  ProGen Pro provides a robust solution that effectively captures dependencies while managing uncertainty. Our experiments on four benchmark traffic datasets demonstrate that ProGen Pro outperforms state-of-the-art deterministic probabilistic models.
  arXiv  Detail & Related papers  (2024-11-02T14:37:30Z)
• When Rigidity Hurts: Soft Consistency Regularization for Probabilistic Hierarchical Time Series Forecasting [69.30930115236228]
  Probabilistic hierarchical time-series forecasting is an important variant of time-series forecasting. Most methods focus on point predictions and do not provide well-calibrated probabilistic forecasts distributions. We propose PROFHiT, a fully probabilistic hierarchical forecasting model that jointly models forecast distribution of entire hierarchy.
  arXiv  Detail & Related papers  (2023-10-17T20:30:16Z)
• User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systems [49.75149094527068]
  We show that diffusion models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. We develop a probabilistic approximation scheme for the conditional score function which converges to the true distribution as the noise level decreases. We are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.
  arXiv  Detail & Related papers  (2023-06-13T03:42:03Z)
• Interpretable reduced-order modeling with time-scale separation [9.889399863931676]
  Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. We propose a data-driven scheme that automates the identification of the time-scales involved. We show that this data-driven scheme can automatically learn the independent processes that decompose a system of linear ODEs.
  arXiv  Detail & Related papers  (2023-03-03T19:23:59Z)
• When Rigidity Hurts: Soft Consistency Regularization for Probabilistic Hierarchical Time Series Forecasting [69.30930115236228]
  Probabilistic hierarchical time-series forecasting is an important variant of time-series forecasting. Most methods focus on point predictions and do not provide well-calibrated probabilistic forecasts distributions. We propose PROFHiT, a fully probabilistic hierarchical forecasting model that jointly models forecast distribution of entire hierarchy.
  arXiv  Detail & Related papers  (2022-06-16T06:13:53Z)
• Distributional Gradient Boosting Machines [77.34726150561087]
  Our framework is based on XGBoost and LightGBM. We show that our framework achieves state-of-the-art forecast accuracy.
  arXiv  Detail & Related papers  (2022-04-02T06:32:19Z)
• Flow-based Spatio-Temporal Structured Prediction of Motion Dynamics [21.24885597341643]
  Conditional Flows (CNFs) are flexible generative models capable of representing complicated distributions with high dimensionality and interdimensional correlations. We propose MotionFlow as a novel approach that autoregressively normalizes the output on the temporal input features. We apply our method to different tasks, including prediction, motion prediction time series forecasting, and binary segmentation.
  arXiv  Detail & Related papers  (2021-04-09T14:30:35Z)
• Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting [98.57851612518758]
  Probabilistic time series forecasting involves estimating the distribution of future based on its history. We propose a deep state space model for probabilistic time series forecasting whereby the non-linear emission model and transition model are parameterized by networks. We show in experiments that our model produces accurate and sharp probabilistic forecasts.
  arXiv  Detail & Related papers  (2021-01-31T06:49:33Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.