Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An unsupervised learning approach to solving heat equations on chip
  based on Auto Encoder and Image Gradient   Solving heat transfer equations on chip becomes very critical in the upcoming
5G and AI chip-package-systems. However, batches of simulations have to be
performed for data driven supervised machine learning models. Data driven
methods are data hungry, to address this, Physics Informed Neural Networks
(PINN) have been proposed. However, vanilla PINN models solve one fixed heat
equation at a time, so the models have to be retrained for heat equations with
different source terms. Additionally, issues related to multi-objective
optimization have to be resolved while using PINN to minimize the PDE residual,
satisfy boundary conditions and fit the observed data etc. Therefore, this
paper investigates an unsupervised learning approach for solving heat transfer
equations on chip without using solution data and generalizing the trained
network for predicting solutions for heat equations with unseen source terms.
Specifically, a hybrid framework of Auto Encoder (AE) and Image Gradient (IG)
based network is designed. The AE is used to encode different source terms of
the heat equations. The IG based network implements a second order central
difference algorithm for structured grids and minimizes the PDE residual. The
effectiveness of the designed network is evaluated by solving heat equations
for various use cases. It is proved that with limited number of source terms to
train the AE network, the framework can not only solve the given heat transfer
problems with a single training process, but also make reasonable predictions
for unseen cases (heat equations with new source terms) without retraining.

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The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph