Solving high-dimensional partial differential equations using deep learning

# Solving high-dimensional partial differential equations using deep learning > OpenAlex Metadata Hub · https://openalex.org/W2803629276 ## Bibliographic - **DOI:** 10.1073/pnas.1718942115 - **Year:** 2018 - **Citations:** 1717 - **Open Access:** Yes (green) - **License:** — - **Source:** https://arxiv.org/pdf/1707.02568 ## Authors - Jiequn Han - Arnulf Jentzen - E Weinan ## Abstract Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality." This paper introduces a deep learning-based approach that can handle general high-dimensional parabolic PDEs. To this end, the PDEs are reformulated using backward stochastic differential equations and the gradient of the unknown solution is approximated by neural networks, very much in the spirit of deep reinforcement learning with the gradient acting as the policy function. Numerical results on examples including the nonlinear Black-Scholes equation, the Hamilton-Jacobi-Bellman equation, and the Allen-Cahn equation suggest that the proposed algorithm is quite effective in high dimensions, in terms of both accuracy and cost. This opens up possibilities in economics, finance, operational research, and physics, by considering all participating agents, assets, resources, or particles together at the same time, instead of making ad hoc assumptions on their interrelationships. ## Keywords Partial differential equation, Deep learning, Computer science, Applied mathematics, Mathematics, Mathematical analysis, Artificial intelligence ## Concepts - Partial differential equation - Deep learning - Computer science - Applied mathematics - Mathematics - Mathematical analysis - Artificial intelligence --- *Metadata only — full text not imported unless Open Access license permits.*

Bài “Solving high-dimensional partial differential equations using deep learning” được TradingBase chuyển thành Knowledge Product cho trader — không phải trang đọc abstract OpenAlex. Tóm lược học thuật (đã diễn giải): Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality." This paper introduces a deep learning-based approach that can handle general high-dimensional parabolic PDEs. To this end, the PDEs are reformulated using backward stochastic differential equations and the gradient of the unknown solution is approximated by neural networks, very much in the spirit of deep reinforcement learning with the gradient acting as the policy function. Numerical results on examples including the nonlinear Black-Scholes equation, the Hamilton-Jacobi-Bellman equation, and the Allen-Cahn equation suggest that the proposed algorithm is quite effective in high dimensions, in terms of both accuracy and cost. This opens up possibilities in economics… Phần Trading Insights bên dưới nối nghiên cứu với Forex, vàng, USD, lãi suất và risk regime — để bạn đưa vào journal và playbook. Metadata DOI/OA chỉ là rail tham chiếu; nội dung chính là summary, takeaways và ứng dụng thị trường do Content Factory sinh.