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Variational Integrator Graph Networks for Learning Energy Conserving Dynamical Systems [article]

Shaan Desai, Marios Mattheakis, Stephen Roberts
2021 arXiv   pre-print
To tackle this problem we unpack and generalize recent innovations into individual inductive bias segments.  ...  integrators, and graph neural networks.  ...  To address this challenge, researchers have shown that enriching neural networks with well-chosen inductive biases such as Hamiltonians [5] , integrators [6-8] and graphs [9] [10] [11] can significantly  ... 
arXiv:2004.13688v2 fatcat:eu2hzv755rezxoagv2y7iakema

SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems [article]

Pengzhan Jin, Zhen Zhang, Aiqing Zhu, Yifa Tang, George Em Karniadakis
2020 arXiv   pre-print
We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules.  ...  We then perform several experiments including the pendulum, double pendulum and three-body problems to investigate the expressivity and the generalization ability of SympNets.  ...  Problem setup We apply a neural network model to learn the phase flow of the Hamiltonian system from data.  ... 
arXiv:2001.03750v3 fatcat:jn2upr2r6fedxl2vvakiynul3y

Identifying Physical Law of Hamiltonian Systems via Meta-Learning [article]

Seungjun Lee, Haesang Yang, Woojae Seong
2021 arXiv   pre-print
A well-modeled Hamiltonian makes it easy for researchers to analyze and forecast many related phenomena that are governed by the same physical law.  ...  We propose that meta-learning algorithms can be potentially powerful data-driven tools for identifying the physical law governing Hamiltonian systems without any mathematical assumptions on the representation  ...  Then, the trajectory of the state can be computed by integrating the symplectic gradient of the Hamiltonian.  ... 
arXiv:2102.11544v1 fatcat:3qhmb2yehjfvfmat27va34wfqu

Which priors matter? Benchmarking models for learning latent dynamics [article]

Aleksandar Botev and Andrew Jaegle and Peter Wirnsberger and Daniel Hennes and Irina Higgins
2021 arXiv   pre-print
Recently, several methods have proposed to integrate priors from classical mechanics into ML models to address the challenge of physical reasoning from images.  ...  To this end, we introduce a suite consisting of 17 datasets with visual observations based on physical systems exhibiting a wide range of dynamics.  ...  Unlike the rigid body assumption, this separability assumption is fairly general and holds for many interesting problems. It allows us to use symplectic integrators which naturally conserve energy.  ... 
arXiv:2111.05458v1 fatcat:aamoqjiup5ee7hgvpzaj5mm7n4

Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data [article]

Marc Finzi, Samuel Stanton, Pavel Izmailov, Andrew Gordon Wilson
2020 arXiv   pre-print
The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems.  ...  While translation equivariance provides a powerful inductive bias for images, we often additionally desire equivariance to other transformations, such as rotations, especially for non-image data.  ...  as an inductive bias, it has a very special implication for the modeling of Hamiltonian systems.  ... 
arXiv:2002.12880v3 fatcat:hjtrai2btreu7inxyiixbrrj74

Some Fundamental Theorems in Mathematics [article]

Oliver Knill
2022 arXiv   pre-print
If M is a finite probability space, then the Vlasov Hamiltonian system is the Hamiltonian n-body problem on N. An other example is M = T * N and where m is an initial phase space measure.  ...  Newton realized that this is governed by a differential equation, the n-body problem x ′′ j (t) = n i=1 c ij (x i − x j ) |x i − x j | 3 , where c ij depends on the masses and the gravitational constant  ...  The simplest is the box counting definition which works for most household fractals: if we need n squares of length r to cover a set, then d = − log(n)/ log(r) converges to the dimension of the set with  ... 
arXiv:1807.08416v4 fatcat:lw7lbsxyznfrnaozilxapihmdy

Recent advances in mechatronics

Okyay Kaynak
1996 Robotics and Autonomous Systems  
The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or  ...  The conference was highly successful, it had more than 200 participants from 34 different countries.  ...  Acknowledgements The authors would like to thank Mr. K. Tonegawa for his help with the experiments.  ... 
doi:10.1016/s0921-8890(96)00039-5 fatcat:l5fd4hwa2rbu3l6f2jucyj2fxy

Inductive Biases in Machine Learning for Robotics and Control

Michael Lutter
To show that incorporating existing knowledge as inductive biases in machine learning algorithms can improve performance, we present three different algorithms: (1) The Differentiable Newton Euler Algorithm  ...  A fundamental problem of robotics is how can one program a robot to perform a task with its limited embodiment? Classical robotics solves this problem by carefully engineering interconnected modules.  ...  ., I had the pleasure to work with amazing researchers that helped me grow and improve my research. Therefore, I would like thank:  ... 
doi:10.26083/tuprints-00020048 fatcat:ukl3tppkybaa7ncigmsiiddtqa

The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning [article]

Yang-Hui He
2020 arXiv   pre-print
to ArXiv for comments and suggestions.  ...  Based on various lecture series, colloquia and seminars given by the author in the past year, this writing is a very preliminary draft of a book to appear with Springer, by whose kind permission we post  ...  and then, added with a bias, will return a 50-vector.  ... 
arXiv:1812.02893v2 fatcat:fvjjtjo2tngjzl6ubuv42f56va

Editor in Chief Co-Editor Editorial Board Maurizio Consoli General Relativity High energy laser interactions with charged particles Classical equation of motion with radiation reaction Electromagnetic radiation reaction forces Foreword i 2 Metric Gauge Fields in Deformed Special Relativity

Ignazio Licata, Ammar Sakaji, Ignazio Licata, Ammar Sakaji, Ammar Sakaji, Ignazio Licata, Gerardo Torres Del Castillo, Leonardo Chiatti, Francisco Chinea, Avshalom Elitzur, Elvira Fortunato, Tepper Gill (+18 others)
2003 Electronic Journal of Theoretical Physics Electronic Journal of Theoretical Physics Ammar Sakaji, Founder and Editor in Chief   unpublished
Acknowledgment The author wishes to thank Prof. Ignazio Licata for the proposed theme, the numerous discussions and suggestions.  ...  Acknowledgment We thank Hrvoje Nikolic and Vinko Zlatic for discussions and debates, which helped very much during writing this essay.  ...  This solution is acceptable for a wide class of problems. For example, the neural network was used for recognition of the handwritten digit highlighted on the screen [28] .  ... 

Interim Design Report [article]

R. J. Abrams, S. K. Agarwalla, A. Alekou, C. Andreopoulos, C. M. Ankenbrandt, S. Antusch, M. Apollonio, M. Aslaninejad, J. Back, P. Ballett, G. Barker, K. B. Beard, E. Benedetto (+117 others)
2011 arXiv   pre-print
The IDS-NF mandate is to deliver the Reference Design Report (RDR) for the facility on the timescale of 2012/13.  ...  The choice of example sites should not be interpreted as implying a preferred choice of site for the facility.  ...  Acknowledgements During the course of the IDS-NF to date, we have been welcomed at a number of laboratories across the world and therefore thank the CERN, FNAL, and RAL laboratories and the Tata  ... 
arXiv:1112.2853v1 fatcat:vrsxihtpnrhe5eulu6n6ynt3wy

Unleashing the power of semantic text analysis: a complex systems approach

Andrea Martini
(1.38) −∞ However, the naive substitution of the sum in Equation 1.35 with the integral induces a problem: although  ...  , induction, and representation of knowledge.  ... 
doi:10.5075/epfl-thesis-8473 fatcat:lw4fclsi4rfhhiwuawytxwx6sy