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Numerical Method (3): PDE Approach*
Feynman–Kac theorem shows the equivalence of an expectation calculation and the solution to the related PDE for option pricing. In this chapter, we...
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Numerical Solution for Sparse PDE Constrained Optimization
In this chapter, elliptic PDE-constrained optimal control problems with L1-control cost (L1-EOCP) are considered. Motivated by the success of the...
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Commutation of Geometry-Grids and Fast Discrete PDE Eigen-Solver GPA
A geometric intrinsic pre-processing algorithm(GPA for short) for solving large-scale discrete mathematical-physical PDE in 2-D and 3-D case has been...
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Numerical Solution for Sparse PDE-Constrained Optimization
In this chapter, elliptic PDE-constrained optimal control problems with L1-control cost (L1-EOCP) are considered. Motivated by the success of the...
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Deep convolutional Ritz method: parametric PDE surrogates without labeled data
The parametric surrogate models for partial differential equations (PDEs) are a necessary component for many applications in computational sciences,...
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A theoretical study of a bilateral term with a tensor-based fourth-order PDE for image super-resolution
In this paper, we study a fourth-order partial differential equation (PDE), where a diffusion tensor is combined with a bilateral total variation...
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A nonsmooth primal-dual method with interwoven PDE constraint solver
We introduce an efficient first-order primal-dual method for the solution of nonsmooth PDE-constrained optimization problems. We achieve this...
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Parameter Identifiability in PDE Models of Fluorescence Recovery After Photobleaching
Identifying unique parameters for mathematical models describing biological data can be challenging and often impossible. Parameter identifiability...
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Structural identifiability analysis of age-structured PDE epidemic models
Computational and mathematical models rely heavily on estimated parameter values for model development. Identifiability analysis determines how well...
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A relaxation-based probabilistic approach for PDE-constrained optimization under uncertainty with pointwise state constraints
We consider a class of convex risk-neutral PDE-constrained optimization problems subject to pointwise control and state constraints. Due to the many...
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Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration
We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal control problems subject to parabolic partial...
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Detecting Two-Dimensional Fingering Patterns in a Non-Equilibrium PDE Model via Adaptive Moving Meshes
AbstractThis article discusses an adaptive mesh method applied to a bifurcation problem in a non-equilibrium Richard’s equation from hydrology. The...
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Travelling Waves in a PDE–ODE Coupled Model of Cellulolytic Biofilms with Nonlinear Diffusion
We analyze travelling wave (TW) solutions for nonlinear systems consisting of an ODE coupled to a degenerate PDE with a diffusion coefficient that...
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Numerical solutions of two-dimensional PDE-constrained optimal control problems via bilinear pseudo-spectral method
A bilinear pseudo-spectral method (BPSM) is proposed for solving two-dimensional parabolic optimal control problems (OCPs). Firstly, the OCP is...
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Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery
In this contribution, we develop an efficient surrogate modeling framework for simulation-based optimization of enhanced oil recovery, where we...
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A PDE Model for Protocell Evolution and the Origin of Chromosomes via Multilevel Selection
The evolution of complex cellular life involved two major transitions: the encapsulation of self-replicating genetic entities into cellular units and...
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Efficient scalarization in multiobjective optimal control of a nonsmooth PDE
This work deals with the efficient numerical characterization of Pareto stationary fronts for multiobjective optimal control problems with a moderate...
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A path-following inexact Newton method for PDE-constrained optimal control in BV
We study a PDE-constrained optimal control problem that involves functions of bounded variation as controls and includes the TV seminorm of the...
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A Second Order Accurate, Positivity Preserving Numerical Method for the Poisson–Nernst–Planck System and Its Convergence Analysis
A second order accurate (in time) numerical scheme is proposed and analyzed for the Poisson–Nernst–Planck equation (PNP) system, reformulated as a...
