Results 81 to 90 of about 28,837 (165)
Differences in mycelial turnover and persistence of wood‐decay fungi at the microscale
New Phytologist, Volume 250, Issue 1, Page 577-590, April 2026.Summary How long do fungal hyphae persist in the environment? And how does this differ between groups and species of fungi? Despite growing knowledge of fungal contributions to decomposition and soil carbon cycles, surprisingly little is known about the turnover of mycelia: What happens to fungal hyphae over time? And how this impacts different fungi's
Roos‐Marie I. J. van Bokhoven +2 more
wiley +1 more source
A Deep Uzawa-Lagrange Multiplier Approach for Boundary Conditions in PINNs and Deep Ritz Methods
Journal of Machine Learning19 pages, 13 figures; updated address of ...
Makridakis, Charalambos G. +2 more
openaire +2 more sources
Finding geodesics with the Deep Ritz method
Geodesic problems involve computing trajectories between prescribed initial and final states to minimize a user-defined measure of distance, cost, or energy. They arise throughout physics and engineering -- for instance, in determining optimal paths through complex environments, modeling light propagation in refractive media, and the study of spacetime
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Existence of Bound States in Continuous 0
, 2001 In modern fundamental theories there is consideration of higher dimensions, often in the context of what can be written as a Schr\"odinger equation. Thus, the energetics of bound states in different dimensions is of interest.
Abramowitz +29 more
core +1 more source
Kernel Methods in the Deep Ritz framework: Theory and practice
In this contribution, kernel approximations are applied as ansatz functions within the Deep Ritz method. This allows to approximate weak solutions of elliptic partial differential equations with weak enforcement of boundary conditions using Nitsche's method.
Kleikamp, Hendrik, Wenzel, Tizian
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Predicting malting barley protein concentration [PDF]
, 2007 The preferred grain protein concentration (CP) of malting barley is 10.5-11.0%, but 9.5-11.5% is acceptable. It is a challenge for farmers to achieve this target with crops grown in heterogeneous fields and exposed to fluctuating weather conditions ...
Pettersson, C.G.
core
Solving parametric PDE problems with artificial neural networks
, 2017 The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modeled into the equations as random coefficients.
Khoo, Yuehaw, Lu, Jianfeng, Ying, Lexing
core +1 more source
Optimal error estimates of a mixed finite element method for\ud parabolic integro-differential equations with non smooth initial data [PDF]
, 2010 In this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to mixed methods for PIDE, the present method does not bank on a reformulation using a resolvent ...
Goswami, D., Pani, A. K., Yadav, S
core
Generalization Error in the Deep Ritz Method with Smooth Activation Functions
Communications in Computational PhysicsThe manuscript presents an in-depth theoretical analysis of the Deep Ritz method (DRM) and addresses the generalization error inherent in this deep learning paradigm for solving partial differential equations (PDEs), focusing specifically on the Poisson equation.
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Journal of Computational ScienceThis paper presents a novel approach that combines the Deep Ritz Method (DRM) with Fourier feature mapping to solve minimization problems comprised of multi-well, non-convex energy potentials. These problems present computational challenges as they lack a global minimum. Through an investigation of three benchmark problems in both 1D and 2D, we observe
Ensela Mema, Ting Wang, Jaroslaw Knap
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