@ARTICLE{10985-23502,
	journal = {Computer Methods in Applied Mechanics and Engineering},
	volume = {409},
	pages = {115972},
	year = {2023},
	author = {JIANG, Jindong and WU, Jiajun and CHEN, Qiang and CHATZIGEORGIOU, George and MERAGHNI, Fodil},
	abstract = {Elements of the periodic homogenization framework and deep neural network were seamlessly connected for the first time to construct a new micromechanics theory for thermoconductive composites called physically informed Deep Homogenization Network (DHN). This method utilizes a two-scale expansion of the temperature field of spatially uniform composites in terms of macroscopic and fluctuating contributions. The latter is estimated using deep neural network layers. The DHN is trained on a set of collocation points to obtain the fluctuating temperature field over the unit cell domain by minimizing a cost function given in terms of residuals of strong form steady-state heat conduction governing differential equations. Novel use of a periodic layer with several independent periodic functions with adjustable training parameters ensures that periodic boundary conditions of temperature and temperature gradients at the unit cell edges are exactly satisfied. Automatic differentiation is utilized to correctly compute the fluctuating temperature gradients. Homogenized properties and local temperature and gradient distributions of unit cells reinforced by unidirectional fiber or weakened by a hole are compared with finite-element reference results, demonstrating remarkable correlation but without discontinuities associated with temperature gradient distributions in the finite-element simulations. We also illustrate that the DHN enhanced with transfer learning provides a substantially more efficient and accurate simulation of multiple random fiber distributions relative to training the network from scratch.},
	issn = {0045-7825},
	edition = {Post-print},
	title = {Physically informed deep homogenization neural network for unidirectional multiphase/multi-inclusion thermoconductive composites},
	publisher = {Elsevier BV},
	url = {10.1016/j.cma.2023.115972}
}

@ARTICLE{10985-25184,
	journal = {Composite Structures},
	volume = {340},
	pages = {118171},
	year = {2024},
	author = {WU, Jiajun and CHEN, Qiang and JIANG, Jindong and CHATZIGEORGIOU, George and MERAGHNI, Fodil},
	abstract = {We present an adaptive physics-informed deep homogenization neural network (DHN) approach to formulate a full-field micromechanics model for elastic and thermoelastic periodic arrays with different microstructures. The unit cell solution is approximated by fully connected multilayers via minimizing a loss function formulated in terms of the sum of residuals from the stress equilibrium and heat conduction partial differential equations (PDEs), together with interfacial traction-free or adiabatic boundary conditions. In comparison, periodicity boundary conditions are directly satisfied by introducing a network layer with sinusoidal functions. Fully trainable weights are applied on all collocation points, which are simultaneously trained alongside the network weights. Hence, the network automatically assigns higher weights to the collocation points in the vicinity of the interface (particularly challenging regions of the unit cell solution) in the loss function. This compels the neural networks to enhance their performance at these specific points. The accuracy of adaptive DHN is verified against the finite element and the elasticity solution respectively for elliptical and circular cylindrical pores/fibers. The advantage of the adaptive DHN over the original DHN technique is justified by considering locally irregular porous architecture where pore–pore interaction makes training the network particularly slow and hard to optimize.},
	issn = {0263-8223},
	edition = {Post-print},
	title = {Adaptive deep homogenization theory for periodic heterogeneous materials},
	publisher = {Elsevier BV},
	url = {10.1016/j.compstruct.2024.118171}
}