A display screen shows information about ChatGPT, a language model for dialogue optimization. The text includes details on how the model is used in conversational contexts. The background is primarily green, with pink and purple graphic lines on the right side. The OpenAI logo is positioned at the top left.
A display screen shows information about ChatGPT, a language model for dialogue optimization. The text includes details on how the model is used in conversational contexts. The background is primarily green, with pink and purple graphic lines on the right side. The OpenAI logo is positioned at the top left.

The expected outcomes of this research include: 1) A neural network-based solver for SPDEs that excels in solving high-dimensional, nonlinear, and highly stochastic equations. 2) Experimental validation demonstrating the solver's versatility and efficiency in fields such as physics and finance, particularly in terms of solving accuracy and computational efficiency. 3) A new theoretical framework and technical tool for the SPDE solving field, advancing related technologies. 4) New application scenarios and optimization ideas for OpenAI’s models and systems, particularly in handling complex mathematical problems. These outcomes will enhance OpenAI models' capabilities in complex system modeling, promoting their applications in more fields.

Innovative Solutions for SPDEs

We develop advanced neural network solvers for stochastic partial differential equations, enhancing accuracy and efficiency through innovative frameworks and experimental validation.

A large, worn out chalkboard filled with complex equations written in white chalk. The equations involve mathematical and physics notations, covering most of the board. The board has a reddish-brown hue with visible wear and scratches.
A large, worn out chalkboard filled with complex equations written in white chalk. The equations involve mathematical and physics notations, covering most of the board. The board has a reddish-brown hue with visible wear and scratches.
A textbook is open to Chapter 6, titled 'Regression Models for Overdispersed Count Response.' The page discusses various statistical models, including the negative binomial regression model, providing mathematical explanations and theoretical backgrounds.
A textbook is open to Chapter 6, titled 'Regression Models for Overdispersed Count Response.' The page discusses various statistical models, including the negative binomial regression model, providing mathematical explanations and theoretical backgrounds.
A complex, swirling mass of thin, tangled lines resembling neural connections or abstract tendrils emerges from the center, set against a stark black background. The lines vary in thickness and length, intertwining with a dynamic flow that suggests movement.
A complex, swirling mass of thin, tangled lines resembling neural connections or abstract tendrils emerges from the center, set against a stark black background. The lines vary in thickness and length, intertwining with a dynamic flow that suggests movement.

Our Research Approach

Our research spans theoretical analysis, algorithm design, and experimental validation, focusing on optimizing neural networks for solving complex stochastic equations.

Innovative Neural Solutions

We develop advanced neural network frameworks for solving stochastic partial differential equations efficiently.

Several sheets of paper with handwritten mathematical notes are placed on a laptop keyboard. The notes include equations and text related to recurrence relations and mathematical induction, written in blue ink. The layout suggests a focus on problem-solving or academic work.
Several sheets of paper with handwritten mathematical notes are placed on a laptop keyboard. The notes include equations and text related to recurrence relations and mathematical induction, written in blue ink. The layout suggests a focus on problem-solving or academic work.
Theoretical Analysis Phase

Studying mathematical properties of SPDEs integrated with neural networks.

Algorithm Design Phase

Creating optimized neural network solvers using physics-informed techniques and variational autoencoders.

Experimental Validation Phase

Testing algorithms on classic SPDEs for accuracy and computational efficiency.

Research

Innovative solutions for stochastic partial differential equations.

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