Related papers: Learning Neural Hamiltonian Dynamics: A Methodolog…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
Rigid body interactions are fundamental to numerous scientific disciplines, but remain challenging to simulate due to their abrupt nonlinear nature and sensitivity to complex, often unknown environmental factors. These challenges call for…
The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically…
Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…
This work introduces a new framework integrating port-Hamiltonian systems (PHS) and neural network architectures. This framework bridges the gap between deterministic and stochastic modeling of complex dynamical systems. We introduce new…
In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. Basic idea is to associate with the incidence matrix of the graph a Dirac…
Hamiltonian learning (HL), enabling precise estimation of system parameters and underlying dynamics, plays a critical role in characterizing quantum systems. However, conventional HL methods face challenges in noise robustness and resource…
A framework for identifying nonlinear port-Hamiltonian systems using input-state-output data is introduced. The framework utilizes neural networks' universal approximation capacity to effectively represent complex dynamics in a structured…
Attractor dynamics are a fundamental computational motif in neural circuits, supporting diverse cognitive functions through stable, self-sustaining patterns of neural activity. In these lecture notes, we review four key examples that…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks…
Reliable autonomous navigation requires adapting the control policy of a mobile robot in response to dynamics changes in different operational conditions. Hand-designed dynamics models may struggle to capture model variations due to a…
A generic data-assisted control architecture within the port-Hamiltonian framework is proposed, introducing a physically meaningful observable that links conservative dynamics to all actuation, dissipation, and disturbance channels. A…
This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the…
A growing body of work leverages the Hamiltonian formalism as an inductive bias for physically plausible neural network based video generation. The structure of the Hamiltonian ensures conservation of a learned quantity (e.g., energy) and…
Hamiltonian parameter estimation is crucial in condensed matter physics, but time and cost consuming in terms of resources used. With advances in observation techniques, high-resolution images with more detailed information are obtained,…
Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions. Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning. This…
Designing neural networks within a Hamiltonian framework offers a principled way to ensure that conservation laws are respected in physical systems. While promising, these capabilities have been largely limited to discrete, analytically…
This thesis explores how deep learning models learn over time, using ideas inspired by force analysis. Specifically, we zoom in on the model's training procedure to see how one training example affects another during learning, like…
Deep learning models are able to approximate one specific dynamical system but struggle at learning generalisable dynamics, where dynamical systems obey the same laws of physics but contain different numbers of elements (e.g., double- and…