Related papers: Exploration of methods for computing sensitivities…
We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an…
The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…
Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior…
In dynamic discrete choice models, some parameters, such as the discount factor, are being fixed instead of being estimated. This paper proposes two sensitivity analysis procedures for dynamic discrete choice models with respect to the…
Solving stiff ordinary differential equations (StODEs) requires sophisticated numerical solvers, which are often computationally expensive. In general, traditional explicit time integration schemes with restricted time step sizes are not…
Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…
This is the second part of four series papers, aiming at the problem of sensor dynamics compensation for abstract linear systems. Two major issues are addressed. The first one is about the sensor dynamics compensation in system observation…
The paper presents a sensitivity analysis of the factors affecting the optimal partitioning of a district heating network for distributed control. Leveraging a physics-based, distributed model predictive control framework and a…
Accurate crowd simulation is crucial for public safety management, emergency evacuation planning, and intelligent transportation systems. However, existing methods, which typically model crowds as a collection of independent individual…
Many industries now deploy high-fidelity simulators (digital twins) to represent physical systems, yet their parameters must be calibrated to match the true system. This motivated the construction of simulation-driven parameter estimators,…
Computing stationary states is an important topic for phase field crystal (PFC) models. Great efforts have been made for energy dissipation of the numerical schemes when using gradient flows. However, it is always time-consuming due to the…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient…
Accurate estimation of parameters is paramount in developing high-fidelity models for complex dynamical systems. Model-based optimal experiment design (OED) approaches enable systematic design of dynamic experiments to generate input-output…
We present an exact approach to analyze and quantify the sensitivity of higher moments of probabilistic loops with symbolic parameters, polynomial arithmetic and potentially uncountable state spaces. Our approach integrates methods from…
Iterative steady-state solvers are widely used in computational fluid dynamics. Unfortunately, it is difficult to obtain steady-state solution for unstable problem caused by physical instability and numerical instability. Optimization is a…
Using vanilla NeuralODEs to model large and/or complex systems often fails due two reasons: Stability and convergence. NeuralODEs are capable of describing stable as well as instable dynamic systems. Selecting an appropriate numerical…
Engineering simulators used for steady-state multiphase pipe flows are commonly utilized to predict pressure drop. Such simulators are typically based on either empirical correlations or first-principles mechanistic models. The simulators…
In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual…
Density matrices evolved according the von Neumann equation are commonly used to simulate the dynamics of driven quantum systems. However, computational methods using density matrices are often too slow to explore the large parameter spaces…