Related papers: Discovering stochastic dynamical equations from bi…
In the study of complex dynamical systems, understanding and accurately modeling the underlying physical processes is crucial for predicting system behavior and designing effective interventions. Yet real-world systems exhibit pronounced…
Real world systems evolve in continuous-time according to their underlying causal relationships, yet their dynamics are often unknown. Existing approaches to learning such dynamics typically either discretize time -- leading to poor…
The dynamics of species' densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include…
Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…
Complex change is often described as "evolutionary" in economics, policy, and technology, yet most system dynamics models remain constrained to fixed state spaces and equilibrium-seeking behavior. This paper argues that evolutionary…
Stochastic evolution underpins several approaches to the dynamics of open quantum systems, such as random modulation of Hamiltonian parameters, the stochastic Schrodinger equation (SSE), and the stochastic Liouville equation (SLE). These…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…
Modeling dynamical systems and unraveling their underlying causal relationships is central to many domains in the natural sciences. Various physical systems, such as those arising in cell biology, are inherently high-dimensional and…
In stochastic dynamical systems, different concepts of stability can be obtained in different limits. A particularly interesting example is evolutionary game theory, which is traditionally based on infinite populations, where strict Nash…
The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…
The discovery of governing differential equations from data is an open frontier in machine learning. The sparse identification of nonlinear dynamics (SINDy) \citep{brunton_discovering_2016} framework enables data-driven discovery of…
Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We…
Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and…
A new stochastic control problem of population dynamics under partial observation is formulated and analyzed both mathematically and numerically, with an emphasis on environmental and ecological problems. The decision-maker can only…
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…
Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future…
We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…
Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the…