相关论文: Kinetics Parameter Optimization via Neural Ordinar…
Model reduction methods are relevant when the computation time of a full convection-diffusion-reaction simulation based on detailed chemical reaction mechanisms is too large. In this article, we review a model reduction approach based on…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…
The inherent slow imaging speed of Magnetic Resonance Image (MRI) has spurred the development of various acceleration methods, typically through heuristically undersampling the MRI measurement domain known as k-space. Recently, deep neural…
Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.…
Although optimal control problems of dynamical systems can be formulated within the framework of variational calculus, their solution for complex systems is often analytically and computationally intractable. In this Letter we present a…
The adaptation of neural codes to the statistics of their environment is well captured by efficient coding approaches. Here we solve an inverse problem: characterizing the objective and constraint functions that efficient codes appear to be…
The high computational cost of evaluating atomic interactions recently motivated the development of computationally inexpensive kinetic models, which can be parametrized from MD simulations of complex chemistry of thousands of species or…
Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…
Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…
Traditionally, calcium dynamics in neurons are modeled using partial differential equations (PDEs) and ordinary differential equations (ODEs). The PDE component focuses on reaction-diffusion processes, while the ODE component addresses…
Mathematical modeling with Ordinary Differential Equations (ODEs) has proven to be extremely successful in a variety of fields, including biology. However, these models are completely deterministic given a certain set of initial conditions.…
Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by…
Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no…
Soft robots have many advantages over rigid robots thanks to their compliant and passive nature. However, it is generally challenging to model the dynamics of soft robots due to their high spatial dimensionality, making it difficult to use…
We introduce two block coordinate descent algorithms for solving optimization problems with ordinary differential equations (ODEs) as dynamical constraints. The algorithms do not need to implement direct or adjoint sensitivity analysis…
We explore in detail a method to solve ordinary differential equations using feedforward neural networks. We prove a specific loss function, which does not require knowledge of the exact solution, to be a suitable standard metric to…
A computation-oriented representation of uncertain kinetic systems is introduced and analysed in this paper. It is assumed that the monomial coefficients of the ODEs belong to a polytopic set, which defines a set of dynamical systems for an…
Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions. Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning. This…
In this paper we introduce a procedure for identifying optimal methods in parametric families of numerical schemes for initial value problems in partial differential equations. The procedure maximizes accuracy by adaptively computing…