A problem specific recurrent neural network for the description and simulation of dynamic spring models

We present a recurrent neural network which was designed for the description and simulation of dynamic spring models. The network simulates the physical behavior of deformable or elastic solids like stiffness, viscosity and inertia. The physical parameters of the real model can be used to initialize the network parameters. Besides, it is possible to learn the deformation behavior of a real solid. Using a neural network structure, local changes to the system like collisions or cuts can be easily performed during simulation. Furthermore, it is possible to speed up the simulation by parallel hardware.

[1]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[2]  C. S. George Lee,et al.  Neural fuzzy systems: a neuro-fuzzy synergism to intelligent systems , 1996 .

[3]  Tommaso Toffoli,et al.  Cellular Automata as an Alternative to (Rather than an Approximation of) Differential Equations in M , 1984 .

[4]  Stephane Cotin,et al.  Real Time Volumetric Deformable Models for Surgery Simulation , 1996, VBC.

[5]  Frank Klawonn,et al.  Foundations of fuzzy systems , 1994 .

[6]  Fernando J. Pineda,et al.  GENERALIZATION OF BACKPROPAGATION TO RECURRENT AND HIGH-ORDER NETWORKS. , 1987 .

[7]  Fernando J. Pineda,et al.  Recurrent Backpropagation and the Dynamical Approach to Adaptive Neural Computation , 1989, Neural Computation.

[8]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[9]  John J. Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities , 1999 .

[10]  Morten Bro-Nielsen,et al.  Surgery Simulation Using fast Finite Elements , 1996, VBC.

[11]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[12]  Ronald J. Williams,et al.  Experimental Analysis of the Real-time Recurrent Learning Algorithm , 1989 .

[13]  Pineda,et al.  Generalization of back-propagation to recurrent neural networks. , 1987, Physical review letters.

[14]  Tommaso Toffoli,et al.  Cellular automata machines - a new environment for modeling , 1987, MIT Press series in scientific computation.

[15]  P. Gould.  Introduction to Linear Elasticity , 1983 .

[16]  Detlef Nauck,et al.  Foundations Of Neuro-Fuzzy Systems , 1997 .

[17]  Christian Kuhn,et al.  Modellbildung und Echtzeitsimulation deformierbarer Objekte zur Entwicklung einer interaktiven Trainingsumgebung für die minimal-invasive Chirurgie , 1997 .

[18]  Zbigniew Wesolowski.  Nonlinear dynamics of elastic bodies , 1978 .

[19]  Arne Radetzky,et al.  Simulation of elastic tissues in virtual medicine using neuro-fuzzy systems , 1998, Medical Imaging.