English
Related papers

Related papers: For differential equations with r parameters, 2r+1…

200 papers

A series of examples of computational models is provided, where the model aim is to interpret numerical results in terms of internal states of agents minds. Two opposite strategies or research can be distinguished in the literature. First…

Physics and Society · Physics 2014-08-26 Krzysztof Kulakowski , Piotr Gronek , Antoni Dydejczyk

Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…

Statistics Theory · Mathematics 2025-04-29 Jie Qi , Ruth E. Baker

Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…

Algebraic Geometry · Mathematics 2014-12-30 Elisenda Feliu

Note: Accepted version, published in Statistical Papers, https://doi.org/10.1007/s00362-023-01414-3. It is shown that some theoretically identifiable parameters cannot be empirically identified, meaning that no consistent estimator of them…

Statistics Theory · Mathematics 2023-04-18 Christian Hennig

To comprehend complex systems with multiple states, it is imperative to reveal the identity of these states by system outputs. Nevertheless, the mathematical models describing these systems often exhibit nonlinearity so that render the…

Machine Learning · Computer Science 2023-07-04 Guangtao Zhang , Yiting Duan , Guanyu Pan , Qijing Chen , Huiyu Yang , Zhikun Zhang

We consider the problem of detecting the true quantum state among $r$ possible ones, based of measurements performed on $n$ copies of a finite-dimensional quantum system. A special case is the problem of discriminating between $r$…

Quantum Physics · Physics 2012-05-14 Michael Nussbaum , Arleta Szkoła

A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal; for example, a video of a chaotic pendulums system. Assuming that we know the dynamical model up to some unknown parameters, can we estimate the…

Machine Learning · Statistics 2021-11-24 Ofir Lindenbaum , Amir Sagiv , Gal Mishne , Ronen Talmon

Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations…

Machine Learning · Statistics 2023-11-03 Megan R. Ebers , Katherine M. Steele , J. Nathan Kutz

Quantifying coherence has received increasing attention, and considerable work has been directed towards finding coherence measures. While various coherence measures have been proposed in theory, an important issue following is how to…

Quantum Physics · Physics 2018-05-02 Da-Jian Zhang , C. L. Liu , Xiao-Dong Yu , D. M. Tong

We present an extension of the identity method initially introduced for particle yield fluctuation studies towards measurements of differential correlations. The extension is developed and illustrated in the context of measurements of the…

Data Analysis, Statistics and Probability · Physics 2018-07-25 Claude Pruneau , Alice Ohlson

This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite-dimensional nuisance parameter. We introduce a…

Statistics Theory · Mathematics 2014-09-24 Isaiah Andrews , Anna Mikusheva

Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations with the use of machine learning techniques. In contrast to classical methods which assume the structure of the…

Machine Learning · Computer Science 2024-10-10 Philipp Scholl , Aras Bacho , Holger Boche , Gitta Kutyniok

Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…

Mathematical Physics · Physics 2011-09-27 H. Azad , A. Laradji , M. T. Mustafa

Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of…

Numerical Analysis · Mathematics 2025-06-10 Roy Y. He , Hao Liu , Wenjing Liao , Sung Ha Kang

The scope of this research is the identification of unknown piecewise constant parameters of linear regression equation under the finite excitation condition. Compared to the known methods, to make the computational burden lower, only one…

Systems and Control · Electrical Eng. & Systems 2022-08-05 Anton Glushchenko , Konstantin Lastochkin

We describe how a single-particle tracking experiment should be designed in order for its recorded trajectories to contain the most information about a tracked particle's diffusion coefficient. The precision of estimators for the diffusion…

Biological Physics · Physics 2016-08-10 Christian L. Vestergaard

Bilinear dynamical systems are ubiquitous in many different domains and they can also be used to approximate more general control-affine systems. This motivates the problem of learning bilinear systems from a single trajectory of the…

Machine Learning · Computer Science 2022-08-31 Yahya Sattar , Samet Oymak , Necmiye Ozay

Model-based experimental design is attracting increasing attention in chemical process engineering. Typically, an iterative procedure is pursued: an approximate model is devised, prescribed experiments are then performed and the resulting…

Optimization and Control · Mathematics 2021-01-25 Charlie Vanaret , Philipp Seufert , Jan Schwientek , Gleb Karpov , Gleb Ryzhakov , Ivan Oseledets , Norbert Asprion , Michael Bortz

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…

Other Computer Science · Computer Science 2016-11-15 Deepyaman Maiti , Ayan Acharya , R. Janarthanan , Amit Konar

In modern scientific research, small-scale studies with limited participants are increasingly common. However, interpreting individual outcomes can be challenging, making it standard practice to combine data across studies using random…

Statistics Theory · Mathematics 2025-11-04 Lucas Kania , Larry Wasserman , Sivaraman Balakrishnan