Data-Driven Inverse Modeling with Incomplete Observations
summary
Presents a method that trains neural nets while enforcing PDE constraints exactly by making both explicit and implicit numerical solvers differentiable with reverse‑mode AD, implemented in ADCME.jl (Julia + TensorFlow backend). Claims faster convergence and greater stability than penalty approaches on stiff problems and demonstrates recovery of space‑dependent parameters and constitutive functions, including differentiable implicit PDE solvers that backpropagate through Newton iterations, successful inference of nonlinear relative‑permeability and fractional orders from sparse data, and estimates functions from four sensors with noise robustness.
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chapters (9)
- 0:00Introduction to talk
- 1:49Inverse modeling basics
- 3:36Physics-informed neural networks
- 8:36Automatic differentiation overview
- 15:01Applications introduction
- 15:21Elastic full waveform inversion
- 21:01Base car elasticity modeling
- 25:38Summary and future work
- 28:12Q&A session
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