Related papers: Dynamical errors in machine learning forecasts

Multi-modal trajectory forecasting methods commonly evaluate using single-agent metrics (marginal metrics), such as minimum Average Displacement Error (ADE) and Final Displacement Error (FDE), which fail to capture joint performance of…

Mixture-of-Experts (MoE) models have shown remarkable capability in instruction tuning, especially when the number of tasks scales. However, previous methods simply merge all training tasks (e.g. creative writing, coding, and mathematics)…

Deep neural networks have shown remarkable performance when trained on independent and identically distributed data from a fixed set of classes. However, in real-world scenarios, it can be desirable to train models on a continuous stream of…

Mixture-of-Experts (MoE) architectures enable conditional computation by routing inputs to multiple expert subnetworks and are often motivated as a mechanism for scaling large language models. In this project, we instead study MoE behavior…

The arrival time prediction of Coronal mass ejections (CMEs) is an area of active research. Many methods with varying levels of complexity have been developed to predict CME arrival. However, the mean absolute error (MAE) of predictions…

Forecasting presents a complex estimation challenge, as it involves balancing multiple, often conflicting, priorities and objectives. Conventional forecast optimization methods typically emphasize a single metric--such as minimizing the…

Reliable dynamic sea level forecasts are hindered by numerous sources of uncertainty on daily-to-seasonal timescales (1-180 days) due to atmospheric boundary conditions and internal ocean variability. Studies have demonstrated that certain…

Data stream forecasts are essential inputs for decision making at digital platforms. Machine learning algorithms are appealing candidates to produce such forecasts. Yet, digital platforms require a large-scale forecast framework that can…

We introduce a new analysis of an adaptive mixture method that combines outputs of two constituent filters running in parallel to model an unknown desired signal. This adaptive mixture is shown to achieve the mean square error (MSE)…

The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…

Several phenomena are available representing market activity: volumes, number of trades, durations between trades or quotes, volatility - however measured - all share the feature to be represented as positive valued time series. When…

We study the effect of fading in the communication channels between sensor nodes on the performance of the incremental least mean square (ILMS) algorithm, and derive steady state performance metrics, including the mean-square deviation…

Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…

Advanced deep learning-based approaches have been actively applied to forecast the spatiotemporal physical dynamics governed by partial differential equations (PDEs), which acts as a critical procedure in tackling many science and…

In this paper, prediction for linear systems with missing information is investigated. New methods are introduced to improve the Mean Squared Error (MSE) on the test set in comparison to state-of-the-art methods, through appropriate tuning…

This paper considers mean square error (MSE) analysis for stochastic gradient sampling algorithms applied to underdamped Langevin dynamics under a global convexity assumption. A novel discrete Poisson equation framework is developed to…

Data-driven weather models have recently achieved state-of-the-art performance, yet progress has plateaued in recent years. This paper introduces a Mixture of Experts (MoWE) approach as a novel paradigm to overcome these limitations, not by…

Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice of the…

Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…

Autonomous vehicles use a variety of sensors and machine-learned models to predict the behavior of surrounding road users. Most of the machine-learned models in the literature focus on quantitative error metrics like the root mean square…