1,917 research outputs found
Lipschitz Optimisation for Lipschitz Interpolation
Techniques known as Nonlinear Set Membership prediction, Kinky Inference or
Lipschitz Interpolation are fast and numerically robust approaches to
nonparametric machine learning that have been proposed to be utilised in the
context of system identification and learning-based control. They utilise
presupposed Lipschitz properties in order to compute inferences over unobserved
function values. Unfortunately, most of these approaches rely on exact
knowledge about the input space metric as well as about the Lipschitz constant.
Furthermore, existing techniques to estimate the Lipschitz constants from the
data are not robust to noise or seem to be ad-hoc and typically are decoupled
from the ultimate learning and prediction task. To overcome these limitations,
we propose an approach for optimising parameters of the presupposed metrics by
minimising validation set prediction errors. To avoid poor performance due to
local minima, we propose to utilise Lipschitz properties of the optimisation
objective to ensure global optimisation success. The resulting approach is a
new flexible method for nonparametric black-box learning. We provide
experimental evidence of the competitiveness of our approach on artificial as
well as on real data
Geometrical Frustration and Static Correlations in Hard-Sphere Glass Formers
We analytically and numerically characterize the structure of hard-sphere
fluids in order to review various geometrical frustration scenarios of the
glass transition. We find generalized polytetrahedral order to be correlated
with increasing fluid packing fraction, but to become increasingly irrelevant
with increasing dimension. We also find the growth in structural correlations
to be modest in the dynamical regime accessible to computer simulations.Comment: 21 pages; part of the "Special Topic Issue on the Glass Transition
Discrete breathers in a nonlinear electric line: Modeling, Computation and Experiment
We study experimentally and numerically the existence and stability
properties of discrete breathers in a periodic nonlinear electric line. The
electric line is composed of single cell nodes, containing a varactor diode and
an inductor, coupled together in a periodic ring configuration through
inductors and driven uniformly by a harmonic external voltage source. A simple
model for each cell is proposed by using a nonlinear form for the varactor
characteristics through the current and capacitance dependence on the voltage.
For an electrical line composed of 32 elements, we find the regions, in driver
voltage and frequency, where -peaked breather solutions exist and
characterize their stability. The results are compared to experimental
measurements with good quantitative agreement. We also examine the spontaneous
formation of -peaked breathers through modulational instability of the
homogeneous steady state. The competition between different discrete breathers
seeded by the modulational instability eventually leads to stationary
-peaked solutions whose precise locations is seen to sensitively depend on
the initial conditions
TANGO: Time-Reversal Latent GraphODE for Multi-Agent Dynamical Systems
Learning complex multi-agent system dynamics from data is crucial across many
domains, such as in physical simulations and material modeling. Extended from
purely data-driven approaches, existing physics-informed approaches such as
Hamiltonian Neural Network strictly follow energy conservation law to introduce
inductive bias, making their learning more sample efficiently. However, many
real-world systems do not strictly conserve energy, such as spring systems with
frictions. Recognizing this, we turn our attention to a broader physical
principle: Time-Reversal Symmetry, which depicts that the dynamics of a system
shall remain invariant when traversed back over time. It still helps to
preserve energies for conservative systems and in the meanwhile, serves as a
strong inductive bias for non-conservative, reversible systems. To inject such
inductive bias, in this paper, we propose a simple-yet-effective
self-supervised regularization term as a soft constraint that aligns the
forward and backward trajectories predicted by a continuous graph neural
network-based ordinary differential equation (GraphODE). It effectively imposes
time-reversal symmetry to enable more accurate model predictions across a wider
range of dynamical systems under classical mechanics. In addition, we further
provide theoretical analysis to show that our regularization essentially
minimizes higher-order Taylor expansion terms during the ODE integration steps,
which enables our model to be more noise-tolerant and even applicable to
irreversible systems. Experimental results on a variety of physical systems
demonstrate the effectiveness of our proposed method. Particularly, it achieves
an MSE improvement of 11.5 % on a challenging chaotic triple-pendulum systems
The Epistemology of Simulation, Computation and Dynamics in Economics Ennobling Synergies, Enfeebling 'Perfection'
Lehtinen and Kuorikoski ([73]) question, provocatively, whether, in the context of Computing the Perfect Model, economists avoid - even positively abhor - reliance on simulation. We disagree with the mildly qualified affirmative answer given by them, whilst agreeing with some of the issues they raise. However there are many economic theoretic, mathematical (primarily recursion theoretic and constructive) - and even some philosophical and epistemological - infelicities in their descriptions, definitions and analysis. These are pointed out, and corrected; for, if not, the issues they raise may be submerged and subverted by emphasis just on the unfortunate, but essential, errors and misrepresentationsSimulation, Computation, Computable, Analysis, Dynamics, Proof, Algorithm
Automated and Sound Synthesis of Lyapunov Functions with SMT Solvers
In this paper we employ SMT solvers to soundly synthesise Lyapunov functions
that assert the stability of a given dynamical model. The search for a Lyapunov
function is framed as the satisfiability of a second-order logical formula,
asking whether there exists a function satisfying a desired specification
(stability) for all possible initial conditions of the model. We synthesise
Lyapunov functions for linear, non-linear (polynomial), and for parametric
models. For non-linear models, the algorithm also determines a region of
validity for the Lyapunov function. We exploit an inductive framework to
synthesise Lyapunov functions, starting from parametric templates. The
inductive framework comprises two elements: a learner proposes a Lyapunov
function, and a verifier checks its validity - its lack is expressed via a
counterexample (a point over the state space), for further use by the learner.
Whilst the verifier uses the SMT solver Z3, thus ensuring the overall soundness
of the procedure, we examine two alternatives for the learner: a numerical
approach based on the optimisation tool Gurobi, and a sound approach based
again on Z3. The overall technique is evaluated over a broad set of benchmarks,
which shows that this methodology not only scales to 10-dimensional models
within reasonable computational time, but also offers a novel soundness proof
for the generated Lyapunov functions and their domains of validity
Fluid Model Checking
In this paper we investigate a potential use of fluid approximation
techniques in the context of stochastic model checking of CSL formulae. We
focus on properties describing the behaviour of a single agent in a (large)
population of agents, exploiting a limit result known also as fast simulation.
In particular, we will approximate the behaviour of a single agent with a
time-inhomogeneous CTMC which depends on the environment and on the other
agents only through the solution of the fluid differential equation. We will
prove the asymptotic correctness of our approach in terms of satisfiability of
CSL formulae and of reachability probabilities. We will also present a
procedure to model check time-inhomogeneous CTMC against CSL formulae
Coupling the Yoccoz-Birkeland population model with price dynamics: chaotic livestock commodities market cycles
We propose a new model for the time evolution of livestock commodities which
exhibits endogenous deterministic stochastic behaviour. The model is based on
the Yoccoz-Birkeland integral equation, a model first developed for studying
the time-evolution of single species with high average fertility, a relatively
short mating season and density dependent reproduction rates. This equation is
then coupled with a differential equation describing the price of a livestock
commodity driven by the unbalance between its demand and supply. At its birth
the cattle population is split into two parts: reproducing females and cattle
for butchery. The relative amount of the two is determined by the spot price of
the meat. We prove the existence of an attractor and we investigate numerically
its properties: the strange attractor existing for the original
Yoccoz-Birkeland model is persistent but its chaotic behaviour depends also
from the price evolution in an essential way.Comment: 26 pages, 19 figure
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