Paper discovers structural dynamics equations from only acceleration data.
problem Discovering equations from only acceleration measurements in structural dynamics.
method Library-based approach with Approximate Bayesian Computation (ABC) prioritizing parsimonious models.
result Efficacy demonstrated in four structural dynamics examples, including linear and nonlinear systems.
New method infers dynamical systems from population data.
problem Inferring dynamical systems from population data.
method Deducing and estimating Fokker-Planck equation, projecting to test functions, sparse inference.
result Induces driving forces of dynamical systems.
Deep learning predicts dynamics from sparse data.
problem Predicting spatiotemporal dynamics from sparse data.
method Spatially dimension-independent deep learning framework.
result Predicts dynamics from sparse data sites.
Stabilized neural differential equations enforce constraints on dynamical systems.
problem Ensuring dynamical systems preserve known constraints like conservation laws.
method SNDEs with a stabilization term to enforce manifold constraints.
result SNDEs outperform existing methods and broaden constraint types.
A new kernel framework analyzes spatio-temporal data from dynamic equations.
problem Analyzing spatio-temporal data from dynamic equations with noisy measurements.
method Kernel-based framework with representer theorem for minimizing error with given samples.
result Minimizes error in solutions of dynamic equations with noisy spatio-temporal data.
RNN operators solve Newton's equations with large timesteps for molecular dynamics.
problem Solving Newton's equations of motion with large timesteps for molecular dynamics simulations.
method Recurrent Neural Networks (RNN) operators to solve Newton's equations using past trajectory data.
result Significant speedup in molecular dynamics simulations with timesteps up to 4000 times larger.
Derives EoM for DNNs to describe GD dynamics precisely.
problem Gaps between differential equations and actual DNN learning dynamics due to discretization error.
method Starts from GF, derives counter term to cancel discretization error, obtains EoM.
result EoM precisely describes GD dynamics of DNNs, highlights differences between continuous and discrete GD.
New research connects evolutionary dynamics to Bayesian learning.
problem Connecting evolutionary biology and Bayesian learning.
method Rigorous mathematical proof using Kushner-Stratonovich equation and gradient flows.
result Discrete time filtering equations converge to Stratonovich interpretation of Kushner-Stratonovich equation.
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of set-valued functionals in the recent literature. There are two possible extensi…
PNDEs project neural dynamics onto constraint manifolds, improving accuracy and stability.
problem Learning dynamics from data without violating known constraints.
method Projecting the learned vector field onto the tangent space of the constraint manifold.
result PNDEs outperform existing methods in learning constrained dynamical systems.
Data-driven approach learns effective equations for phase field interfaces.
problem Learning accurate equations for phase field interface dynamics.
method Data-driven identification of partial differential equations from phase field data.
result Data-driven equations outperform analytical approximations in certain regimes.
Improved latent dynamics identification framework reduces training time and improves accuracy.
problem Accurate numerical solutions of partial differential equations require computationally expensive solvers.
method Sequential decoder training (mLaSDI) to correct residual errors from previous stages.
result mLaSDI consistently outperforms standard LaSDI, achieving lower prediction errors and reduced training time.
Derives equations of motion for systems with angular momentum on Finsler geometries.
problem Equations of motion for dynamical systems with angular momentum on Finsler geometries.
method Apply Souriau's Principle of General Covariance to derive diffeomorphism invariant equations of motion.
result Generalizes Mathisson-Papapetrou-Dixon equations to Finsler geometries and finds conserved quantities.
PySR method automates discovering equations from data in chaotic dynamics and epidemics.
problem Discovering equations from complex data in dynamical systems.
method Symbolic regression methods, focusing on PySR.
result PySR method efficiently infers equations from chaotic dynamics and epidemic models, matching original forms.
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian dynamical system in a manifold, one can consider it as geometric equipment of this manif…
A Gaussian Process Ordinary Differential Equation framework for large continuous dynamical systems
problem Forecasting complex dynamical systems
method Kernel autonomous ODE approach based on Gaussian Processes and Quadratic Order Model Reduction
result Full model outperforms ROM methods in terms of accuracy or computational costs
Neural networks improve predictions of complex network dynamics.
problem Improving neural network predictions for complex network dynamics.
method Extended neural network models to complex systems, ensuring they conform to dynamical model assumptions and using a statistical significance test.
result Achieved advanced generalization of neural network predictions for complex systems.
Neural GDEs improve graph prediction by blending discrete structures and differential equations.
problem Dynamic graph prediction challenges in irregularly sampled data.
method Continuous-depth graph neural networks (GNNs) with Neural GDEs.
result Neural GDEs enhance performance across various applications.
Graph neural controlled differential equations learn graph dynamics from vertex observations.
problem Predicting future states of dynamical systems on graphs with limited vertex data.
method Incorporates graph topology information into NCDE to predict graph dynamics.
result Informed NCDE requires fewer parameters and lower MAE compared to previous methods.
Neural differential equations combine deep learning and differential equations for modeling complex systems.
problem Modeling complex systems with high capacity and efficiency.
method Combining neural networks and differential equations, focusing on neural ordinary, controlled, and stochastic differential equations.
result NDEs offer high-capacity function approximation, strong priors, and handle irregular data efficiently.
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points are moving along rays. As it appears, their motion can be described by Hamilton e…
This paper studies the Yang--Mills ASD equation over the cylinder as a non-linear evolution equation. We consider a dynamical system consisting of bounded orbits of this evolution equation. This system contains many chaotic orbits, and moreover it becomes an infinite dimensional and infinite entropy system. We study th…
A method uses non-autonomous equations to classify time signals efficiently.
problem Time signal classification with minimal parameters and high accuracy.
method Develops a framework using non-autonomous dynamical equations to classify time signals.
result The method achieves comparable accuracy with fewer parameters than existing methods.
Proposes a new test for validating multivariate dynamic regression models.
problem Inadequate exogeneity conditions for conventional model specification tests in dynamic systems.
method Develops a generalized Durbin estimator for multiple-equation systems with dynamic dependencies, and constructs Wald tests.
result Bootstrap-based Wald tests improve finite-sample size control and validate the null hypothesis in multifactor models.
Construct intrinsic Langevin dynamics for rigid inclusions on curved surfaces.
problem Stochastic dynamics of rigid inclusions on curved surfaces.
method Cartan's method of moving frames, Hamiltonian equations, intrinsic Langevin equations, Fokker-Planck equation.
result Extracted overdamped equations for accurate simulations of diffusion processes.
Study of influenza A virus spread using mathematical equations.
problem Understanding the spread of influenza A virus infection.
method Mathematical model and analysis of dynamical system.
result Surface trajectories and asymptotic behavior of the system.
The paper analyzes convergence of Langevin dynamics with time-dependent metrics.
problem Analyzing convergence of Langevin dynamics with time-dependent metrics.
method Formulated a modified gradient flow of the Kullback-Leibler divergence, selected a time-dependent relative Fisher information functional, and developed a time-dependent Hessian matrix condition.
result Proved convergence conditions for various Langevin dynamics.
Framework infers Langevin dynamics from stochastic observations of latent systems.
problem Inferring non-stationary Langevin dynamics from indirect stochastic observations.
method Non-parametric framework explicitly modeling stochastic observation process and non-stationary latent dynamics.
result Correct inference of non-stationary dynamics requires accounting for non-equilibrium states and observation duration.
Model stock price dynamics using semi-Markov processes.
problem Model stock price dynamics through a semi-Markov process.
method Use semi-Markov process with Poisson random measure, establish existence and uniqueness of solution, derive HJB equation.
result Obtain expressions for optimal controls and value function using HJB equation.
The system of weak normality equations constitutes a part in the complete system of normality equations. Solutions of each of these two systems of equations are associated with some definite classes of Newtonian dynamical systems in Riemannian manifolds. In this paper for the case of simplest flat Riemannian manifold $…
Two effective methods for writing the dynamical equations for non-holonomic systems are illustrated. They are based on the two types of representation of the constraints: by parametric equations or by implicit equations. They can be applied to linear as well as to non-linear constraints. Only the basic notions of vecto…
New method learns soliton dynamics from scattering data without assuming known equations.
problem Deriving soliton dynamics from scattering data without prior knowledge.
method Combining IST with weak-form system identification for data-driven discovery.
result Effective soliton dynamics models derived from observed scattering data.
Develops path integral for spiked tensor model dynamics.
problem Dynamics of spiked tensor model with random initial conditions.
method Path integral approach applied to partial differential equations.
result Large-N saddle point equations dominated by melonic diagrams. The goal of this article is to describe the concepts of system dynamics and its applications to the simulation modeling of financial institutions daily activity. The hybrid method of the re-engineering of banking business processes based upon combination of system dynamics, queuing theory and tools of ordinary differen…
The Ricci flow is a parabolic evolution equation in the space of Riemannian metrics of a smooth manifold. To some extent, Einstein equations give rise to a similar hyperbolic evolution. The present text is an introductory exposition to Bianchi-Ricci and Bianchi-Einstein flows, that is, the restricted finitely dimension…
New model explains market dynamics with phase transitions and non-linear interactions.
problem Understanding complex multi-asset market dynamics with phase transitions.
method Developed a Multi-Asset Non-Equilibrium Skew (MANES) model based on Langevin dynamics and McKean-Vlasov equation.
result The model accurately predicts market returns and phase transitions in both benign and distressed markets.
In this work we present a new approach on studying dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have research the generalized fractional hybrid equations. We have introduced the concepts of generalized fractional Wiener process, generaliz…
Normality equations describe Newtonian dynamical systems admitting normal shift of hypersurfaces. They were first derived in Euclidean geometry, then in Riemannian geometry. Recently they were rederived in more general case, when geometry of manifold is given by generalized Legendre transformation. As appears, in this …
Motivated by the geospin matrix W as a new variable in Riemannian geometry. Then, we use four real dynamical variables {a,α,v,W} to show the dynamical essence of Cartan structural equation, we obtain the geometrodynamics on Riemannian manifolds that can be expressed below \begin{align} & Θ/d{{t}^{2}}…
SINDy-PI robustly identifies implicit dynamics from noisy data.
problem Accurately modeling nonlinear dynamics from noisy data.
method Parallel, implicit SINDy algorithm with multiple optimization algorithms and model selection.
result Significantly more noise robust than previous SINDy approaches.
Neural SVEs model complex systems with memory, outperforming traditional methods.
problem Modeling systems with memory effects and irregular behavior.
method Introducing neural stochastic Volterra equations as a physics-inspired architecture.
result Neural SVEs outperform neural SDEs and DeepONets in various applications.
Novel method estimates complex nonlinear systems with stochastic differential equations.
problem Handling complex nonlinear dynamical systems with strong learning guarantees.
method Estimates drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled stochastic differential equations.
result Strong theoretical guarantees including finite-sample bounds for various metrics.
We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a clas…
In this note we survey some recent results for the Euler equations in compressible and incompressible fluid dynamics. The main point of all these theorems is the surprising fact that a suitable variant of Gromov's h-principle holds in several cases.
Study connects symmetries in dynamical systems to phase plane representations.
problem Understanding symmetries in dynamical systems and their phase plane realizations.
method Analysis of symmetries in differential equations and phase plane representations, establishing correspondence and lifting conditions.
result Every symmetry generator in one formulation corresponds uniquely to a generator in the other, with a lifting condition to solve.
Normality equations describe Newtonian dynamical systems admitting normal shift of hypersurfaces. These equations were first derived in Euclidean geometry. Then very soon they were rederived in Riemannian and in Finslerian geometry. Recently I have found that normality equations can be derived in geometry given by clas…
Develops a dynamic mean field theory for reinforcement learning.
problem Finite state and action Bayesian reinforcement learning in large state spaces.
method Analogies with statistical physics, interpreting probabilities as couplings and values as spins, solving mean field equations.
result State-action values are statistically independent in the asymptotic state space limit, with exact or approximate equations for computation.
Machine learning recently has been used to identify the governing equations for dynamics in physical systems. The promising results from applications on systems such as fluid dynamics and chemical kinetics inspire further investigation of these methods on complex engineered systems. Dynamics of these systems play a cru…