This paper develops an algebraic structure for systems of systems and networks.
problem Formalizing interactions between complex systems and networks.
method Developing a monoidal double category of surjective submersions to encompass systems and maps between them.
result Recovering results on fibrations of networks of manifolds as a special case.
Novel algorithm for optimal control of nonlinear systems.
problem Optimal control of nonlinear stochastic dynamical systems with unknown dynamics.
method Decoupled data-based approach combining open-loop and closed-loop control.
result Performance of D2C algorithm is approximately optimal and significantly reduces training time.
New learning methods for open systems with variable agents.
problem Learning in open systems with dynamic agent arrivals and departures.
method Formulated a unified open-system bandit problem with general dynamics, introducing new concepts like pre-training degree and stability.
result Certified global-UCB learning methodologies with provable guarantees, revealing dependencies between entry uncertainty, stability, and agent patterns.
The financial market entropy is modeled using open quantum systems.
problem Understanding entropy in financial market dynamics.
method Using Open Quantum Systems to model entropy gain in financial markets.
result Interesting non-classical results generated by relaxing assumptions.
Researchers dissect Neural ODEs to understand their dynamics.
problem Understanding the inner workings of Neural ODEs.
method Developing continuous-depth formulation to clarify design choices.
result Clarified the influence of design choices on Neural ODE dynamics.
Paper bridges quantum and classical mechanics for open systems.
problem Quantum open systems with bi-Lindblad structure.
method Develops a bridge between bi-Hamiltonian structures and GKSL formalism, introducing contact-compatible Lindblad generators.
result Provides a mathematical mechanism for semiclassical limit of quantum open systems.
Paper tackles dynamic open world recognition in online settings.
problem Dynamic open world recognition in online settings.
method Incremental learning of the underlying metric, incremental estimate of confidence thresholds, local learning.
result Proposed methods outperform non-online counterparts in various scenarios.
Invariant measures found for contact Hamiltonian systems split into Reeb and Liouville dynamics.
problem Finding invariant measures for contact Hamiltonian systems.
method Splitting the system into Reeb and Liouville dynamics; using invariant measures and symplectic sandwiches.
result Invariant measure found for Reeb dynamics; characterization of Liouville dynamics invariant measure.
New method learns dynamical systems efficiently using active learning.
problem Efficiently learning dynamical systems from data.
method Active learning strategies leveraging Gaussian process regression.
result Data-efficient training of the model through exploratory sampling.
Mathematical model predicts international trade and global economy dynamics.
problem Understanding complex international trade and economy interactions.
method Developed a mathematical model for non-equilibrium processes in open systems.
result Predicted model accurately reflects international trade and economy.
Protocol for quantum reinforcement learning in various quantum systems.
problem Efficient quantum control and machine learning calculations.
method Proposes a protocol for quantum reinforcement learning in multiqubit and multilevel systems, without requiring coherent feedback.
result Protocol enables implementation in diverse quantum systems, including trapped ions and superconducting circuits.
A new framework reduces inconsistencies in chaotic surrogate modeling.
problem Consistency issues between probabilistic objectives and dynamical system dynamics.
method KAFFEE (Kalman-Aware Framework For Ergodic Emulation), a differentiable extended Kalman filter.
result KAFFEE mitigates the dynamic-probabilistic consistency gap, improving reconstruction and predictive scores.
Study on estimating unstable open-loop matrices from state trajectories.
problem System identification for stochastic continuous-time dynamics.
method Employing randomized control inputs to estimate unstable open-loop matrix.
result Estimation error decays with trajectory length, signal-to-noise ratio, and excitability.
Survey on computational models in dynamical systems, including new universality concepts.
problem Understanding the relationship between computational models and dynamical systems.
method Review of recent works on Turing universality, Topological Kleene Field Theories, and dynamical bordisms.
result Introduction of new perspectives on computability through dynamical systems.
Integrable dynamics explained via geometric maps and cluster algebras.
problem Integrable dynamics in projective geometry.
method Twisted triple crossing diagram maps and cluster integrable systems.
result Cross-ratio dynamics described by geometric R-matrices. Efficient algorithm reduces control system learning regret to sqrt(T).
problem Learning Linear-Quadratic Regulators with unknown dynamics efficiently.
method First computationally-efficient algorithm with sqrt(T) regret.
result Resolves open question on control system learning.
Combining causality, control, and reinforcement learning for system control.
problem Learning to control dynamical systems using causal, control, and reinforcement learning approaches.
method Combining causal identification, control strategies, and reinforcement learning to control dynamical systems.
result Combining different learning paradigms for effective system control.
We study the dynamics of the vector field on an open surface given by the gradient of a Green's function. This dynamical approach enables us to show that this field induces an invariant decomposition of the surface as the union of a disk and a 1-skeleton that encodes the topology of the surface. We analyze the structur…
Advocates a local feedback approach for RL in unknown systems.
problem Finding optimal feedback laws in unknown nonlinear dynamical systems.
method Searches over a local feedback representation consisting of an open-loop sequence and an optimal linear feedback law.
result Results in highly efficient training and superior performance compared to global methods.
Model for open, decentralized network with task load balancing.
problem Complex computational tasks in open, decentralized networks.
method Incentive-based load balancing using economic mechanisms.
result Optimized resource allocation and enhanced system resilience.
We investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann sphere due to the automatic coopeartion of many kinds of maps in the system, ev…
A reinforcement learning approach prepares quantum squeezed states in open spin systems.
problem Generating non-classical states in open quantum systems with dissipation and dephasing.
method Reinforcement learning to determine optimal control pulses for spin-squeezing.
result Optimal control sequences enhance collective spin squeezing and entanglement.
SymODEN learns physical systems dynamics from data.
problem Learning dynamics of physical systems from limited data.
method Physics-informed deep learning with Hamiltonian dynamics and control.
result SymODEN generalizes well with fewer samples and interpretable models.
HCLM framework uses entropy regularization for open learning systems.
problem Real-world AI challenges and limitations of deep learning.
method Dynamical and information-theoretic framework with entropy regularization.
result Geometric entropy surrogates, especially log-determinant covariance entropy, induce stronger and more stable information forces.
New framework optimizes forecasting and decision-making in dynamic systems.
problem Optimizing forecasting and decision-making processes in dynamic systems.
method Closed-loop framework using bilevel optimization.
result The proposed methodology yields consistently better performance than the standard open-loop approach.
Develops theory for data-driven methods in dynamical systems.
problem Lack of analysis for data-driven methods in dynamical systems.
method Establishes existence of mapping and properties of operator learning architecture.
result Novel universal approximation theorems for smoothing and forecasting.
New method learns cell trajectories and network interactions from single-cell data.
problem Network inference in systems biology from steady-state data.
method Min-entropy estimation for stochastic dynamics, leveraging both temporal and perturbational data.
result Jointly learns cellular trajectories and network interactions.
One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact propagation of marginals for prediction. This paper addresses two questions left open by t…
Survey of AI in finance covering models, strategies, and knowledge systems.
problem Challenges in applying AI to financial markets, especially in high-frequency trading.
method Systematic analysis of financial AI across predictive models, decision frameworks, and knowledge augmentation systems.
result Critical trade-offs and gaps between theoretical advances and practical implementation in financial AI.
The paper explores the geometry of holomorphic flows and orbits.
problem Understanding the local geometry of holomorphic flows and their equilibria.
method Analyzing the local geometry of first-order equilibria and higher-order equilibria under holomorphic conditions.
result Holomorphic Poincaré-Bendixson theorem: bounded non-periodic orbits are homoclinic or heteroclinic.
AdaptOn achieves logarithmic regret in adaptive control of unknown partially observable linear systems.
problem Adaptive control in partially observable linear dynamical systems.
method AdaptOn algorithm that estimates system dynamics through online learning and gradient descent.
result AdaptOn achieves a logarithmic regret bound of polylog(T) after T steps.
A new method extracts features and reconstructs moments in dynamical systems using information geometry.
problem Reconstructing moments in dynamical systems efficiently and accurately.
method Information-geometric approach on spaces of probability measures.
result Moments can be expanded in eigenfunctions of a kernel integral operator, enabling nonparametric forecasting.
Machine learning identified 13 key equations for distillation column dynamics.
problem Identify governing laws for complex engineered systems.
method Sparse Identification of Non-Linear Dynamics (SINDy) applied to distillation column data.
result Reduced 1000s of equations to 13 interpretable terms.
This paper proposes a geometry-aware active learning framework for spatiotemporal dynamic systems.
problem Challenges in modeling complex dynamic systems with 3D geometries and time evolution.
method Geometry-aware spatiotemporal Gaussian Process (G-ST-GP) and adaptive active learning strategy.
result The proposed framework outperforms traditional methods in predicting high-dimensional dynamic behaviors.
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.
This work uses neural networks and time-stepping to discover nonlinear dynamics from data.
problem Automating the creation of predictive models from large data sets.
method Combining neural networks with multi-step time-stepping schemes.
result Accurately learned dynamics, future state forecasting, and basin of attraction identification.
Deep learning models learn chaotic system dynamics from real and simulated data.
problem Training deep learning models for chaotic systems requires big data.
method Jointly train deep neural networks on real and simulated data, enforcing physical laws.
result Proposes knowledge-based deep learning (KDL) for accurate forecasting of chaotic systems.
This paper reviews information theory in open-world machine learning.
problem Lack of a unified theoretical foundation for open-world machine learning.
method Synthesis of information theoretic approaches.
result Established a pathway toward provable and trustworthy open world intelligence.
This paper analyzes the complexity of deep neural networks using topological entropy and chaos theory.
problem Understanding the complexity and dynamics of deep neural networks.
method Modeling DNN as a discrete-time dynamical system and analyzing its complexity through topological entropy and Lyapunov exponents.
result Properties of DNN dynamics are linked to its classification and generalization capabilities.
New method learns stochastic thermodynamics from system currents.
problem Understanding entropy production in complex dynamical systems.
method Constructs learning framework using currents and machine learning loss functions.
result Derives loss functions for thermodynamic functions directly from dynamics.
Geometric proof for averaging theorem on Riemannian manifolds.
problem Averaging theorem for perturbed dynamical systems on Riemannian manifolds.
method Geometric proof using a free coordinate approach.
result Generalization of averaging procedure to any open domain with compact closure.
Connection found between signal processing and slime mold dynamics.
problem Convergence of IRLS algorithm remains an open problem.
method Connection between IRLS and Physarum dynamics, proving convergence of a damped version.
result Convergence and complexity bounds for a damped version of the IRLS algorithm.
A new framework models and simulates multibody systems using factor graphs.
problem Solving kinematic and dynamic problems for multi-body systems.
method Factor graph theory for modeling and simulation of multibody systems.
result The proposed framework provides a unified approach for multibody systems.
Novel framework for systemic risk analysis in financial markets.
problem Systemic risk in financial markets.
method Multi-scale network dynamics, transfer entropy networks, agent-based modeling, wavelet decomposition, Model Context Protocol (MCP).
result Multi-scale approach reveals hidden systemic risk patterns.
Generative models accelerate molecular dynamics by four orders of magnitude.
problem Femtosecond time steps limit access to slow molecular processes.
method Deep generative modeling framework that accelerates sampling.
result Quantitative characterization of equilibrium ensembles and dynamical relaxation processes.
We show that the planar circular restricted three body problem is of restricted contact type for all energies below the first critical value (action of the first Lagrange point) and for energies slightly above it. This opens up the possibility of using the technology of Contact Topology to understand this particular dy…
CoinTossX is a low-latency, open-source matching engine for financial trading.
problem Efficiently matching orders in financial markets with low latency and high throughput.
method Developed in Java, orders submitted via UDP SBE, low-latency message transport (Aeron Media Driver). Separates order generation and matching.
result Demonstrated low-latency, high-throughput performance in various deployment scenarios.
Survey on moduli spaces of differentials from algebraic geometry perspective.
problem Understanding the topology of moduli spaces of differentials remains limited.
method Algebraic geometry perspective, connections to various fields.
result Many open problems and connections to other fields.