Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Actor-Critic Algorithm for High-dimensional Partial Differential
  Equations   We develop a deep learning model to effectively solve high-dimensional
nonlinear parabolic partial differential equations (PDE). We follow Feynman-Kac
formula to reformulate PDE into the equivalent stochastic control problem
governed by a Backward Stochastic Differential Equation (BSDE) system. The
Markovian property of the BSDE is utilized in designing our neural network
architecture, which is inspired by the Actor-Critic algorithm usually applied
for deep Reinforcement Learning. Compared to the State-of-the-Art model, we
make several improvements including 1) largely reduced trainable parameters, 2)
faster convergence rate and 3) fewer hyperparameters to tune. We demonstrate
those improvements by solving a few well-known classes of PDEs such as
Hamilton-Jacobian-Bellman equation, Allen-Cahn equation and Black-Scholes
equation with dimensions on the order of 100.

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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org