Related papers: Information-driven transitions in projections of u…

In the theoretical modelling of a physical system a crucial step consists in the identification of those degrees of freedom that enable a synthetic, yet informative representation of it. While in some cases this selection can be carried out…

Model-based controllers on real robots require accurate knowledge of the system dynamics to perform optimally. For complex dynamics, first-principles modeling is not sufficiently precise, and data-driven approaches can be leveraged to learn…

Complex dynamical systems driven by the unravelling of information can be modelled effectively by treating the underlying flow of information as the model input. Complicated dynamical behaviour of the system is then derived as an output.…

Efficiently estimating system dynamics from data is essential for minimizing data collection costs and improving model performance. This work addresses the challenge of designing future control inputs to maximize information gain, thereby…

Data-driven modeling can suffer from a constant demand for data, leading to reduced accuracy and impractical for engineering applications due to the high cost and scarcity of information. To address this challenge, we propose a progressive…

The representations of conditional entropy and conditional mutual information are significant in explaining the unique effects among variables. While previous studies based on conditional contrastive sampling have effectively removed…

Nonequilibrium physics encompasses a broad range of natural and synthetic small-scale systems. Optimizing transitions of such systems will be crucial for the development of nanoscale technologies and may reveal the physical principles…

High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on…

The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with model…

While diffusion models excel at generating high-quality samples, their latent variables typically lack semantic meaning and are not suitable for representation learning. Here, we propose InfoDiffusion, an algorithm that augments diffusion…

A method for data-driven interpolatory model reduction is presented in this extended abstract. This framework enables the computation of the transfer function values at given interpolation points based on time-domain input-output data only,…

Unsupervised learning plays an important role in many fields, such as artificial intelligence, machine learning, and neuroscience. Compared to static data, methods for extracting low-dimensional structure for dynamic data are lagging. We…

Dynamical systems with high intrinsic dimensionality are often characterized by extreme events having the form of rare transitions several standard deviations away from the mean. For such systems, order-reduction methods through projection…

We present a representation learning algorithm that learns a low-dimensional latent dynamical system from high-dimensional \textit{sequential} raw data, e.g., video. The framework builds upon recent advances in amortized inference methods…

Compressed sensing techniques enable efficient acquisition and recovery of sparse, high-dimensional data signals via low-dimensional projections. In this work, we propose Uncertainty Autoencoders, a learning framework for unsupervised…

We introduce a notion of usable information contained in the representation learned by a deep network, and use it to study how optimal representations for the task emerge during training. We show that the implicit regularization coming from…

Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…

A popular approach for predicting the future of dynamical systems involves mapping them into a lower-dimensional "latent space" where prediction is easier. We show that the information-theoretically optimal approach uses different mappings…

Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional…