The solution of inverse problems
summary
Gradient-descent methods are implemented in Python 2.7 implementation and applied to real datasets: chirps (time and frequency domain), LIGO gravitational-wave traces from LIGO GW150914, and resonant ultrasonic spectroscopy from www.us-biomat.com. The presentation compares stochastic vs systematic GD, shows stochastic runs (about 200 stochastic runs) producing a cloud of near solutions, demonstrates parameter extraction up to ~10 dimensions by splitting subproblems, and reports when frequency-domain fitting or constrained variable selection avoids local minima and yields usable parameter estimates and model confirmation.
AI-written summary · about
chapters (14)
- 0:00Inverse problems intro
- 1:14What is an inverse problem
- 3:50Direct vs inverse examples
- 8:13Key elements of inverse problems
- 12:45Optimization algorithms
- 14:51Gradient descent explained
- 19:56Python gradient descent
- 20:59Linear regression with gradient descent
- 24:153D parameter space
- 24:58Chirp signal fitting
- 28:08Frequency domain transformation
- 30:13High-dimensional inverse problems
- 32:18Key takeaways
- 33:27Q&A
related talks
46mAnalyzing Optimization and Generalization in Deep Learning via Trajectories of Gradient Descent
43mBlack holes and gravitational waves are discovered (also) with Python!
45mSolving Inverse Problems with Deep Learning
35mThresholds of Descending Algorithms in Inference Problems
46mGradient Descent: The Ultimate Optimizer
01h 30mA Primer on Gaussian Processes for Regression Analysis
29mImplicit Regularization in Nonconvex Statistical Estimation
32mData-Driven Inverse Modeling with Incomplete Observations