Develops methods to simulate rare transitions in molecular systems.
problem Rare transitions between metastable states in molecular systems are difficult to study due to limited data.
method Two novel methods: chain-based and midpoint-based approaches.
result Demonstrates effectiveness of methods in both data-rich and data-scarce scenarios.
Reservoir computing predicts rare critical transitions in complex systems.
problem Predicting rare critical transitions in multiscale dynamical systems.
method Data-driven approach using reservoir computing.
result Successfully predicts critical transitions several time steps in advance.
Deep reinforcement learning method finds rare events in complex systems.
problem Computing transition pathways in high-dimensional systems.
method Formulated as a cost minimization problem, solved using DDPG with physical properties.
result Efficiently samples and computes globally optimal transition pathways.
Study identifies transitions between traffic modes on Cologne motorways.
problem Understanding transitions between different traffic modes.
method Constructed state transition network, identified dominant states using PageRank algorithm.
result Identified seasonal dependence in traffic modes.
The paper tackles joint learning of linear systems, improving accuracy with pooled data.
problem Estimating transition matrices of multiple related linear systems more accurately.
method Developed novel techniques to bound estimation errors and establish high probability bounds for singular values.
result Significant gains in accuracy achieved by pooling data across systems.
Machine learning approximates phase transitions using Fisher information.
problem Understanding phase transitions from data using machine learning.
method Information geometry and Fisher information.
result Machine learning indicators approximate the square root of Fisher information.
New transitions found in Spin(7) holonomy metrics related to a dynamical system.
problem Understanding the geometry of Spin(7) holonomy metrics with Aloff--Wallach spaces.
method Relating Spin(7)-equations to a 3-dimensional dynamical system.
result Discovered new transitions with Spin(7) holonomy metrics.
Machine learning predicts synchronization transitions in unknown systems.
problem Predicting synchronization transitions in systems with unknown equations.
method Developed a 'parameter-aware' machine learning scheme using reservoir computing or echo state networks.
result Machine learning accurately predicts synchronization transitions, including hysteresis loops.
We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution, decoupling the transition function from the system states. This is not exact in gene…
This research improves dynamical systems understanding by identifying latent states and their nonlinear transitions.
problem Previous work on dynamical systems could not identify nonlinear transition dynamics, leading to unreliable predictions.
method Proposes a state-space modeling framework using variational auto-encoders to identify latent states and their nonlinear transition functions.
result Demonstrates high accuracy in recovering latent state dynamics and future prediction accuracy.
We give a polynomial-time algorithm for learning latent-state linear dynamical systems without system identification, and without assumptions on the spectral radius of the system's transition matrix. The algorithm extends the recently introduced technique of spectral filtering, previously applied only to systems with a…
Neural models learn continuous-time Markov chain transition rates from data.
problem Learning transition rates for complex stochastic systems.
method Neural networks to model nonlinear transition rates from observed data.
result Neural models outperform traditional methods in accuracy.
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions. Building on previous work on the Hamiltonian theory of impact, we tackle the prob…
New methods use machine learning to simulate rare transitions in molecular systems.
problem Simulating rare transitions between metastable states in molecular dynamics.
method Generative models and reinforcement learning for importance sampling.
result Efficiently generated transition paths linking metastable states.
Persistent entropy detects phase transitions in complex systems.
problem Detecting phase transitions in complex systems.
method Established a general theorem for persistent entropy to reliably detect phase transitions, introduced operational framework for finite-time computations.
result Persistent entropy exhibits an asymptotically non-vanishing gap across phases, robust numerical signatures across experiments.
Deep reinforcement learning finds optimal learning policies for adaptive systems.
problem Finding individualized learning plans for learners with unknown latent traits.
method Formulated as a Markov decision process, applied deep Q-learning with a transition model estimator.
result The algorithm efficiently discovers optimal learning policies with small data sets.
Projective naturality proved for Heegaard Floer homology.
problem Proving naturality of Heegaard Floer invariants under diffeomorphisms.
method Showed Heegaard Floer invariants yield functors to transitive systems in a projectivized category of Z[U]-modules. result Established Heegaard Floer invariants as functors to transitive systems in a projectivized category.
We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects of the MMD. In particular, we show that a formal approximation of the MMD near …
Improved simulation of phase transitions using hierarchical autoregressive networks.
problem Simulating phase transitions in complex systems.
method Hierarchical Autoregressive Neural (HAN) network sampling algorithm.
result Significant improvement in statistical uncertainty compared to the Wolff cluster algorithm.
Paper uses deep learning to compute committor functions for rare events in complex systems.
problem Computing committor functions for low-temperature, high-dimensional systems is challenging.
method Combines deep learning, data sampling, and feature engineering.
result Achieves good performance on complex benchmark problems with rough energy landscapes.
Machine learning detects regime shifts in online game-experiments with high accuracy.
problem Detecting regime shifts in online social systems.
method Gradient-boosted decision trees with memory-retaining features.
result Significantly outperforms standard early warning indicators.
The paper studies dynamical systems with evolving geometric structure using numerical methods.
problem Qualitative behavior of ODEs with varying geometric structure.
method Fourth-order Runge-Kutta scheme for numerical analysis.
result Qualitative transitions in system dynamics as rotation parameter varies.
New STH distance finds patterns in event timeseries without resampling.
problem Lack of efficient analysis methods for event and state timeseries.
method Define STE-ts, propose STH, leveraging both time and state duration.
result Improved precision and computation time compared to resampled metrics.
Manually authoring transition animations for a complete locomotion system can be a tedious and time-consuming task, especially for large games that allow complex and constrained locomotion movements, where the number of transitions grows exponentially with the number of states. In this paper, we present a novel approac…
ISOKANN learns collective variables and effective dynamics for metastable transitions.
problem Understanding metastable transitions in complex molecular systems.
method Integrates Koopman operators with neural networks to extract CVs and effective dynamics.
result Reconstructs coarse-grained kinetics and reproduces transition times across barriers.
Enhances neural network dynamics to boost computational capacity.
problem Improving computational capacity of neural networks.
method Introducing Phase Transition Adaptation to drive system dynamics towards edge of stability.
result Consistently achieves enhancement in computational capacity over multiple datasets.
Study finds a phase transition in flash crashes involving large and liquid stocks.
problem Systemic risk and propagation of shocks in high frequency trading.
method In-depth investigation of co-crashes in high frequency trading.
result Large co-crashes involve mostly illiquid stocks, while small crashes involve a mix of liquid and illiquid stocks.
High-dimensional random geometry shows phase transitions in various problems.
problem Phase transitions in high-dimensional random geometry.
method Analysis of various financial, optimization, and ecological problems.
result Links between seemingly distant fields and further ramifications.
Study analyzes stock market dynamics using recurrence measures and transitions.
problem Understanding transitions in stock market dynamics during crises.
method Recurrence plots and networks from nonstationary stock market data.
result Recurrence measures capture transitions in stock market dynamics.
Novel approach detects early warning indicators in complex systems.
problem Detecting abrupt transitions in complex systems.
method Directed anisotropic diffusion map and latent stochastic dynamical systems.
result Early warning indicators can detect tipping points in state transitions.
Proposes a new model for time series that considers smooth transitions between states.
problem Models assume instantaneous transitions between discrete states, ignoring gradual changes.
method Dynamical Wasserstein Barycentric (DWB) model that estimates system state and pure state distributions over time.
result Accurately learns pure state distributions and improves state estimation for transition periods.
Quasi-equilibrium models for aggregate variables are widely-used throughout finance and economics. The validity of such models depends crucially upon assuming that the systems' participants behave both independently and in a Markovian fashion. We present a simplified market model to demonstrate that herding effects bet…
In Maslov (2003), a two level model of the occurrence of financial pyramid (bubbles) has been considered. We also considered the mathematical analogy of this model to Bose condensation. In the present paper, we explain why Ponzi schemes and bubbles result in a crisis in real economics. In Maslov (2005), the law of incr…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based …
Abstract: Study Hamiltonian systems on almost cosymplectic manifolds, extending contact Hamiltonian systems.
problem Extend Hamiltonian systems to almost cosymplectic manifolds.
method Determine Hamiltonian vector field on odd-dimensional almost cosymplectic manifolds.
result Extend equations of motion to generalized transitive almost cosymplectic structures.
Method detects phase transitions in financial markets using eigenvalue decomposition.
problem Detecting tipping points and fluctuation patterns in financial markets.
method Eigenvalue decomposition and eigen-entropy from cross-correlation matrix.
result Market events undergo phase separation and order-disorder transitions.
Unified framework detects change-points and estimates parameters in nonlinear systems with regime switching.
problem Detecting change-points and estimating parameters in nonlinear dynamical systems with regime transitions.
method Residual-loss anomaly analysis of physics-informed neural networks, two-stage strategy.
result The method outperforms traditional approaches in change-point localization and parameter estimation accuracy.
LoRA fine-tuning causes forgetting, studied via particle system dynamics.
problem Catastrophic forgetting in LoRA fine-tuning.
method Mean-field self-attention model, partial differential equations, dynamical systems.
result Characterization of phase transitions in forgetting behavior.
We analyze the time series of four major cryptocurrencies (Bitcoin, Ethereum, Litecoin, and Ripple) before the digital market crash at the end of 2017 - beginning 2018. We introduce a methodology that combines topological data analysis with a machine learning technique -- k-means clustering -- in order to automatical…
Develops a machine learning framework for computing most probable paths in stochastic systems.
problem Computing the most probable paths in stochastic dynamical systems.
method Reformulates the boundary value problem of Hamiltonian systems and uses a neural network to solve the Euler-Lagrange equation for the Onsager-Machlup action functional.
result Demonstrates the efficacy and accuracy of the machine learning approach in computing most probable paths for stochastic systems with various types of noise.
Change-point analysis is a flexible and computationally tractable tool for the analysis of times series data from systems that transition between discrete states and whose observables are corrupted by noise. The change-point algorithm is used to identify the time indices (change points) at which the system transitions …
Defines SETR to measure carbon transition risk for investors.
problem Difficulty in measuring the magnitude of carbon transition risk for investors.
method Defines Single Event Transition Risk (SETR) and illustrates its use.
result SETR can approximate the magnitude of low-carbon transition risk.
At the heart of technology transitions lie complex processes of social and industrial dynamics. The quantitative study of sustainability transitions requires modelling work, which necessitates a theory of technology substitution. Many, if not most, contemporary modelling approaches for future technology pathways overlo…
Definition of frustration is expressed by transitivity of binary entanglement relation in considered complex system. Extending this definition into n-ary relation a hierarchy of frustrations is derived. As a complex system the U.S. Intermarket is chosen where the correlation coefficient of intermarket sectors plays the…
CNMs detect tipping points in complex systems using causal network markers.
problem Identifying tipping points ahead of critical transitions in complex systems.
method Introducing CNMs that incorporate causality indicators to detect tipping points.
result CNMs show higher predictive power and accuracy than traditional DNB indicators.
A new method eliminates miscalibration in Gaussian process models for dynamical systems.
problem Miscalibration and overestimation of transition function parameters in Gaussian process models.
method Explicitly models the dependence between state trajectories and Gaussian process posterior, eliminating factorization.
result Better predictive performance and more calibrated estimates of the transition function.
Machine learning detects tipping points in complex systems.
problem Detecting abrupt shifts in complex dynamical systems.
method Equilibrium-informed neural networks (EINNs) trained on candidate equilibrium states.
result EINNs can identify critical thresholds in nonlinear systems.
If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure. We define such a phase transition as splitting an underlying manifold into two sub-manifolds with distinct…