Related papers: Learning dynamical systems with hit-and-run random…

The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which…

We can, and should, do statistical inference on simulation models by adjusting the parameters in the simulation so that the values of {\em randomly chosen} functions of the simulation output match the values of those same functions…

Well known to the machine learning community, the random feature model is a parametric approximation to kernel interpolation or regression methods. It is typically used to approximate functions mapping a finite-dimensional input space to…

Task and motion planning (TAMP) frameworks address long and complex planning problems by integrating high-level task planners with low-level motion planners. However, existing TAMP methods rely heavily on the manual design of planning…

In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of…

The use of artificial neural networks as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how neural networks learn chaos is lacking. Here, we employ a geometric perspective to show that neural…

The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…

We show that learning can be improved by using loss functions that evolve cyclically during training to emphasize one class at a time. In underparameterized networks, such dynamical loss functions can lead to successful training for…

Randomized methods of neural network learning suffer from a problem with the generation of random parameters as they are difficult to set optimally to obtain a good projection space. The standard method draws the parameters from a fixed…

A key challenge in satisficing planning is to use multiple heuristics within one heuristic search. An aggregation of multiple heuristic estimates, for example by taking the maximum, has the disadvantage that bad estimates of a single…

As neural networks are increasingly being applied to real-world applications, mechanisms to address distributional shift and sequential task learning without forgetting are critical. Methods incorporating network expansion have shown…

Topological maps are favorable for their small storage compared to geometric map. However, they are limited in relocalization and path planning capabilities. To solve this problem, a feature-based hierarchical topological map (FHT-Map) is…

Undirected graphical models are widely used to model the conditional independence structure of vector-valued data. However, in many modern applications, for example those involving EEG and fMRI data, observations are more appropriately…

A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…

We consider the efficiency of multiplexing spatially encoded information across random configurations of a metasurface-programmable chaotic cavity in the microwave domain. The distribution of the effective rank of the channel matrix is…

Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…

Deep functional maps have emerged in recent years as a prominent learning-based framework for non-rigid shape matching problems. While early methods in this domain only focused on learning in the functional domain, the latest techniques…

A visual system has to learn both which features to extract from images and how to group locations into (proto-)objects. Those two aspects are usually dealt with separately, although predictability is discussed as a cue for both. To…

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have…