9 papers · ranked by Valyu relevance
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
Andrea Polo-Rodríguez, David R. Penas, Julio R. Banga
Parameter estimation is a central challenge in systems biology, particularly for large dynamic models described by nonlinear ordinary differential equations (ODEs). These global optimization problems exhibit landscapes which are topologically heterogeneous, often exhibiting a pathological mixture of stiff, smooth…
Sungho Shin, Ophelia Venturelli, Victor M. Zavala
We present a nonlinear programming (NLP) framework for the scalable solution of parameter estimation problems that arise in dynamic modeling of biological systems. Such problems are computationally challenging because they often involve highly nonlinear and stif differential equations as well as many experimental data…
Alejandro F. Villaverde, Fabian Fröhlich, Daniel Weindl, Jan Hasenauer + 1 more
Mechanistic kinetic models usually contain unknown parameters, which need to be estimated by optimizing the fit of the model to experimental data. This task can be computationally challenging due to the presence of local optima and ill-conditioning. While a variety of optimization methods have been suggested to…
Niklas Neubrand, Timo Rachel, Tim Litwin, Jens Timmer + 2 more
Systems biology strives to unravel the complex dynamics of cellular processes, often with the help of ordinary differential equations (ODEs). However, the sparsity of measured data and the strong non-linearity of common ODEs introduce severe numerical problems in typical modeling tasks. This gave rise to the…
Helge Hass, Carolin Loos, Elba Raimundez Alvarez, Jens Timmer + 2 more
Dynamic models are used in systems biology to study and understand cellular processes like gene regulation or signal transduction. Frequently, ordinary differential equation (ODE) models are used to model the time and dose dependency of the abundances of molecular compounds as well as interactions and translocations. A…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and adaptability needed for emerging imaging technologies and clinical insights. We…
Jane Kondev, Marc Kirschner, Hernan G. Garcia, Gabriel L. Salmon + 1 more
Many biological processes can be thought of as the result of an underlying dynamics in which the system repeatedly undergoes distinct and abortive trajectories with the dynamical process only ending when some specific process, purpose, structure or function is achieved. A classic example is the way in which…
Peter L. Bartlett, Chris Junchi Li, Jingfeng Wu, Bin Yu
In the field of optimization, developing accelerated methods for solving minimax and fixed-point problems remains a fundamental challenge. This paper presents a novel family of dual accelerated algorithms that achieve optimal convergence rates for both minimax and fixed-point problems. By exploring new anchoring…