Yiran Wang
University of Alabama, AL·Mathematics & Statistics
Predicting how heat spreads through a room, how gas drifts through air, or how fluid flows through a complex material means solving partial differential equations (PDEs). PDEs are equations that describe how quantities change across space and time.
- Fields
Mathematics & Statistics
Computer Science
Engineering
- Topics
partial differential equations
reduced order modeling
neural networks
- Grants
- 1 known grant, through Sep 2029
What they work on
- Develop hybrid reduced order models in which neural networks add basis functions to precomputed multiscale ones, guided by stable Petrov-Galerkin formulations and residual-based error indicators.
- Create transfer learning methods that reuse neural network features across families of related nonlinear PDEs. These methods would adapt cheaply to new coefficients, sources, boundaries, geometries or random inputs instead of retraining.
- Design similarity measures based on operator information, spectral behavior and learned features that decide when transfer between related equations is appropriate.
- Build fast adaptive surrogate models for high-dimensional, multiscale problems and test them on predicting temperature, gas concentration and airflow transport fields for autonomous robotics.
More about the research
When a problem has many variables, uncertain inputs or fine-scale detail, these calculations can become too slow for decisions that need answers quickly. This project proposes mathematical and artificial intelligence methods that make such simulations faster while staying accurate and consistent with the underlying physics.
Why it matters
Faster and reliable PDE solvers could let engineers and scientists test many more scenarios and update predictions as conditions change. Possible uses include environmental forecasting and engineering design. They could also help make autonomous robots safer by letting them respond in time to changing heat, gas and airflow around them.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Haomin Zhou
Georgia Institute of Technology, GA·Mathematics & Statistics
Establish parameterized Wasserstein sub-manifolds, which represent evolving probability distributions through a neural network's parameters via a push-forward map and pullback metric, and develop their mathematical foundations.
Tamer Zaki
Johns Hopkins University, MD·Engineering
Develop evolutional deep neural network (EDNN) algorithms that solve high-dimensional partial differential equations by evolving network parameters according to the governing physics, without relying on training data.
Bo Dong
University of Massachusetts-Dartmouth, MA·Mathematics & Statistics
Analyze a new conservative discontinuous Galerkin (DG) method that preserves conserved quantities through implicit penalty parameters, applied to the Korteweg-de Vries equation for shallow-water waves.
The school
University of Alabama: 22 labs on PI Pages, $221M a year on research, 235 research doctorates a year.
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