Related papers: Prediction in Projection
The Koopman operator framework provides a perspective that non-linear dynamics can be described through the lens of linear operators acting on function spaces. As the framework naturally yields linear embedding models, there have been…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
This work addresses fundamental issues related to the structure and conditioning of linear time-delayed models of non-linear dynamics on an attractor. While this approach has been well-studied in the asymptotic sense (e.g. for infinite…
Accurately forecasting the weather is a key requirement for climate change mitigation. Data-driven methods offer the ability to make more accurate forecasts, but lack interpretability and can be expensive to train and deploy if models are…
Application for semantic segmentation models in areas such as autonomous vehicles and human computer interaction require real-time predictive capabilities. The challenges of addressing real-time application is amplified by the need to…
Modern weather forecast models perform uncertainty quantification using ensemble prediction systems, which collect nonparametric statistics based on multiple perturbed simulations. To provide accurate estimation, dozens of such…
Predicting the motion of dynamic agents is a critical task for guaranteeing the safety of autonomous systems. A particular challenge is that motion prediction algorithms should obey dynamics constraints and quantify prediction uncertainty…
We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal approximation of the empirical…
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems…
We present a numerical method to model dynamical systems from data. We use the recently introduced method Scalable Probabilistic Approximation (SPA) to project points from a Euclidean space to convex polytopes and represent these projected…
An efficient representation of observed data has many benefits in various domains of engineering and science. Representing static data sets, such as images, is a living branch in machine learning and eases downstream tasks, such as…
Accurate weather prediction is essential for many aspects of life, notably the early warning of extreme weather events such as rainstorms. Short-term predictions of these events rely on forecasts from numerical weather models, in which,…
Time series data is a prevalent form of data found in various fields. It consists of a series of measurements taken over time. Forecasting is a crucial application of time series models, where future values are predicted based on historical…
Human movement prediction is difficult as humans naturally exhibit complex behaviors that can change drastically from one environment to the next. In order to alleviate this issue, we propose a prediction framework that decouples short-term…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…
Effective representation of data is crucial in various machine learning tasks, as it captures the underlying structure and context of the data. Embeddings have emerged as a powerful technique for data representation, but evaluating their…
The recent developments of complex deep learning models have led to unprecedented ability to accurately predict across multiple data representation types. Conformal prediction for uncertainty quantification of these models has risen in…
Video prediction is a crucial task for intelligent agents such as robots and autonomous vehicles, since it enables them to anticipate and act early on time-critical incidents. State-of-the-art video prediction methods typically model the…
Various neural network based methods are capable of anticipating human body motions from data for a short period of time. What these methods lack are the interpretability and explainability of the network and its results. We propose to use…