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Reproducing kernel Hilbert space method is utilized in this paper as an efficient approach to solve singular fourth order ...

Abstract: Neural Ordinary Differential Equations (NODEs) revolutionize the way we view residual networks as solvers for initial value problems (IVPs), with layer depth serving as the time step. In ...

Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly challenging class of mathematical problems with broad implications for ...

Abstract: This article proposes a stabilization scheme for a cascaded parabolic partial differential equation (PDE)-ordinary differential equation (ODE) system with state constraints. To begin, by ...

Mathematician Ivan Remizov from HSE University–Nizhny Novgorod and the Institute for Information Transmission Problems of the Russian Academy of Sciences has made a conceptual breakthrough in the ...

The Modelica_LinearSystems2 library is a Modelica package providing different representations of linear, time invariant differential and difference equation systems. For example, record StateSpace ...

The tfc Python module is designed to help you quickly and easily apply the Theory of Functional Connections (TFC) to optimization problems. For more information on the code itself and code-based ...

LaFollette, Kyle J., Janni Yuval, Roey Schurr, David Melnikoff, and Amit Goldenberg. "Data-driven Equation Discovery Reveals Nonlinear Reinforcement Learning in Humans." Proceedings of the National ...

Scientific research is a continuous journey fueled by curiosity and collaboration, a conversation between scientists that often crosses continents and spans decades, with each new discovery inspired ...