Prof. Anima Anandkumar on Twitter: "Thanks @jnpmartel Indeed the two lines of work have nice connections. Incorporating AutoInt framework for inverse problems using neural operator would be one interesting application. @ZongyiLiCaltech @kazizzad… https://t.co/pJGYAl4s7s"

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Introducing "Automatic Integration (AutoInt)": a new method using neural networks to learn closed-form solutions to integrals. http://www.computationalimaging.org/publications/automatic-integration/ … We demonstrate AutoInt for neural volume rendering, achieving >10x speedup compared to NeRF! (1/n) @jnpmartel @GordonWetzsteinpic.twitter.com/OOgPzN3pdB

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‏ @AnimaAnandkumar

Replying to @DaveLindell @jnpmartel @GordonWetzstein

Really interesting! Also interesting connections to our neural operator for PDEs since solution operators of PDEs are integral operators. For linear PDE, we have Green's function. For non-linear PDE: composition of linear operators: our neural operatorhttps://twitter.com/AnimaAnandkumar/status/1319055677260611586?s=20 …

Prof. Anima Anandkumar @AnimaAnandkumar

Fourier neural operator for PDEs https://arxiv.org/abs/2010.08895 Solves family of #PDE from scratch at any resolution. Outperforms all existing #DeepLearning methods. 1000x faster than traditional solvers Experiments on Navier-Stokes equations @kazizzad @Caltech #AI #HPC https://twitter.com/arXiv_Daily/status/1318645827460603904 … pic.twitter.com/oOS0EiLdwd

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‏ @jnpmartel

Replying to @AnimaAnandkumar @DaveLindell @GordonWetzstein

David and I, have been impressed by Neural Fourier Operators: this line of work is very inspiring. AutoInt is in the continuity of our SIRENs (NeurIPS'20) where we also solve PDEs with "implicit representations" w/o generalization yet (contrary to NFO)https://twitter.com/vincesitzmann/status/1273409377395859456 …

1:39

Vincent Sitzmann @vincesitzmann

Excited to share our work on "Implicit Neural Representations with Periodic Activations" http://vsitzmann.github.io/siren We show how to fit complex signals, such as room-scale SDFs, video, & audio, and supervise implicit reps via their gradients to solve boundary value problems! (1/n) pic.twitter.com/5Ob57C4Hqg

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