Elena V. Orlova

Ruoxi Jiang, Peter Y. Lu, Elena Orlova et al. · mit

Chaotic systems make long-horizon forecasts difficult because small perturbations in initial conditions cause trajectories to diverge at an exponential rate. In this setting, neural operators trained to minimize squared error losses, while capable of accurate short-term forecasts, often fail to reproduce statistical or structural properties of the dynamics over longer time horizons and can yield degenerate results. In this paper, we propose an alternative framework designed to preserve invariant measures of chaotic attractors that characterize the time-invariant statistical properties of the dynamics. Specifically, in the multi-environment setting (where each sample trajectory is governed by slightly different dynamics), we consider two novel approaches to training with noisy data. First, we propose a loss based on the optimal transport distance between the observed dynamics and the neural operator outputs. This approach requires expert knowledge of the underlying physics to determine what statistical features should be included in the optimal transport loss. Second, we show that a contrastive learning framework, which does not require any specialized prior knowledge, can preserve statistical properties of the dynamics nearly as well as the optimal transport approach. On a variety of chaotic systems, our method is shown empirically to preserve invariant measures of chaotic attractors.

Elena Orlova, Haokun Liu, Raphael Rossellini et al.

Producing high-quality forecasts of key climate variables, such as temperature and precipitation, on subseasonal time scales has long been a gap in operational forecasting. This study explores an application of machine learning (ML) models as post-processing tools for subseasonal forecasting. Lagged numerical ensemble forecasts (i.e., an ensemble where the members have different initialization dates) and observational data, including relative humidity, pressure at sea level, and geopotential height, are incorporated into various ML methods to predict monthly average precipitation and two-meter temperature two weeks in advance for the continental United States. For regression, quantile regression, and tercile classification tasks, we consider using linear models, random forests, convolutional neural networks, and stacked models (a multi-model approach based on the prediction of the individual ML models). Unlike previous ML approaches that often use ensemble mean alone, we leverage information embedded in the ensemble forecasts to enhance prediction accuracy. Additionally, we investigate extreme event predictions that are crucial for planning and mitigation efforts. Considering ensemble members as a collection of spatial forecasts, we explore different approaches to using spatial information. Trade-offs between different approaches may be mitigated with model stacking. Our proposed models outperform standard baselines such as climatological forecasts and ensemble means. In addition, we investigate feature importance, trade-offs between using the full ensemble or only the ensemble mean, and different modes of accounting for spatial variability.

Elena Orlova, Aleksei Ustimenko, Ruoxi Jiang et al.

This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schrödinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit computational complexity that scales exponentially in the problem dimension, our method allows us to adapt to the latent low-dimensional structure of the wave function by sampling from the Markovian diffusion. Depending on the latent dimension, our method may have far lower computational complexity in higher dimensions. Moreover, we propose novel equations for stochastic quantum mechanics, resulting in quadratic computational complexity with respect to the number of dimensions. Numerical simulations verify our theoretical findings and show a significant advantage of our method compared to other deep-learning-based approaches used for quantum mechanics.