Related papers: Dynamical errors in machine learning forecasts
Column-integrated moist static energy (MSE) budgets underpin theories of tropical convection and circulation, yet in reanalyses and climate models the budget rarely closes; residuals routinely match the leading terms and mask physical…
We consider $d$-dimensional linear stochastic approximation algorithms (LSAs) with a constant step-size and the so called Polyak-Ruppert (PR) averaging of iterates. LSAs are widely applied in machine learning and reinforcement learning…
This paper investigates the optimization problem of an infinite stage discrete time Markov decision process (MDP) with a long-run average metric considering both mean and variance of rewards together. Such performance metric is important…
In this paper, we compare the performance of two scenario-based numerical methods to solve stochastic optimal control problems: scenario trees and particles. The problem consists in finding strategies to control a dynamical system perturbed…
AI weather prediction has advanced rapidly, yet no unified mathematical framework explains what determines forecast skill. Existing theory addresses specific architectural choices rather than the learning pipeline as a whole, while…
Recently, data-driven weather forecasting methods have received significant attention for surpassing the RMSE performance of traditional NWP (Numerical Weather Prediction)-based methods. However, data-driven models are tuned to minimize the…
Real-world time series exhibit temporally structured uncertainty: volatility clusters in turbulent regimes, dissipates in stable periods, and shifts abruptly around structural breaks. Yet many probabilistic forecasting methods estimate…
The effectiveness of univariate forecasting models is often hampered by conditions that cause them stress. A model is considered to be under stress if it shows a negative behaviour, such as higher-than-usual errors or increased uncertainty.…
Diffusion models often degrade when trained in latent spaces (e.g., VAEs), yet the formal causes remain poorly understood. We quantify latent-space diffusability through the rate of change of the Minimum Mean Squared Error (MMSE) along the…
Modern deep-learning models have achieved remarkable success in time-series forecasting. Yet, their performance degrades in long-term prediction due to error accumulation in autoregressive inference, where predictions are recursively used…
Accurate forecasts of macroeconomic and financial data, such as GDP, CPI, unemployment rates, and stock indices, are crucial for the success of countries, businesses, and investors, resulting in a constant demand for reliable forecasting…
Machine learning (ML) models are increasingly used in various applications, from recommendation systems in e-commerce to diagnosis prediction in healthcare. In this paper, we present a novel dynamic framework for thinking about the…
The moment conditions or estimating equations for instrumental variables quantile regression involve the discontinuous indicator function. We instead use smoothed estimating equations (SEE), with bandwidth $h$. We show that the mean squared…
Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…
Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate…
The estimation of the parameters of a dynamic signal, such as a sine wave, based on quantized data is customarily performed using the least-square estimator (LSE), such as the sine fit. However, the characteristics of the experiments and…
Subseasonal forecasting of the weather two to six weeks in advance is critical for resource allocation and advance disaster notice but poses many challenges for the forecasting community. At this forecast horizon, physics-based dynamical…
In the last decade, machine learning techniques have gained popularity for estimating causal effects. One machine learning approach that can be used for estimating an average treatment effect is Double/debiased machine learning (DML)…
This paper studies identification and estimation of a class of dynamic models in which the decision maker (DM) is uncertain about the data-generating process. The DM surrounds a benchmark model that he or she fears is misspecified by a set…
Resilience broadly describes a quality of withstanding perturbations. Measures of system resilience have gathered increasing attention across applied disciplines, yet existing metrics often lack computational accessibility and…