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Self-Supervised Learning with Lie Symmetries for Partial Differential Equations

Neural Information Processing Systems

Accurately analyzing and predicting the evolution of such systems is of paramount importance, inspiring decades of innovation in algorithms for numerical methods. However, high-accuracy solvers are often computationally expensive.


Variational Gaussian Processes For Linear Inverse Problems: Supplementary material

Neural Information Processing Systems

The results from one experiment are presented in Figure 2. We plot the resulting variational approximation of the posterior for The conclusions we draw from this experiment are the same as those in Section 4. With the optimal On the left-hand side of Figure 3, we also report the computation times of the methods, and we highlight that the true posterior takes much longer than any of the variational approximations. Again, similar conclusions can be drawn as in the previous sections. Computed T omography (CT) Imaging and Medical Single Photon Emission Computed T omography (SPECT): In CT scans, X-ray measurements are taken from different angles around a patient, and the Radon transform is used to reconstruct a cross-sectional image (slice) of the patient's body. This helps doctors visualize internal structures and diagnose various medical conditions. The Radon transform is used in the image reconstruction process for SPECT.


A Generation Examples

Neural Information Processing Systems

Green indicates factual, red indicates nonfactual, and striked text indicates repetition. So ci ety es ti mates that more than 228,000 peo ple will be di ag nosed with lung can cer in the United... That would make an oxygen mask one of the more popular treatments for this devastating disease. It helps ease breathing and give patients back their strength. The symptoms of lung cancer may resemble those of a bad cold or pneumonia.


The Download: clean energy progress, and OpenAI's trilemma

MIT Technology Review

"We were very much impressed. At the same time, we were afraid." Inside the quest to map the universe with mysterious bursts of radio energy When our universe was less than half as old as it is today, a burst of energy that could cook a sun's worth of popcorn shot out from somewhere amid a compact group of galaxies. Some 8 billion years later, radio waves from that burst reached Earth and were captured by a sophisticated low-frequency radio telescope in the Australian outback. The signal, which arrived in June 2022, and lasted for under half a millisecond, is one of a growing class of mysterious radio signals called fast radio bursts. In the last 10 years, astronomers have picked up nearly 5,000 of them.