Source: https://www.linkedin.com/feed/update/urn%3Ali%3Ashare%3A6815730691259600896
Solve #PDE’s Faster Using #Fourier #Space instead of #Euclidean #Space: https://lnkd.in/eCgMJUu: PDF: https://lnkd.in/ef-R9ze:
#MIT #AI, #ML, #DL, #NLP, #RPA, #Robotics Executive Guide: #Strategy #Road #Maps to #Implementations: https://lnkd.in/eknKzm5 :
#PDE #Fourier #Transforms in:
#Quantitative #Finance: https://lnkd.in/eDPAX-W
#Quantum #Computing: https://lnkd.in/e4T7i2w
#Engineering https://lnkd.in/emVqtKJ
#Physics https://lnkd.in/e2BQm2x
#Science: https://lnkd.in/euqtj9G:
#Mathematical #Quantitative #Finance #Quantum #Computing #Engineering #Physics #Science R&D: SSRN: 82 Top-10 Rankings, Top-1 % Authors: https://lnkd.in/gFn4Vm2 :
R&D Impact Among #AI #Quant #FinTech Nobel Laureates: https://lnkd.in/e-brb8h .
#Partial #differential #equations, PDEs, describe change over #space and #time for #physical phenomena in #universe used to #model planetary orbits to plate tectonics to air turbulence. They are however notoriously hard to solve, highly complex and computationally intensive, requiring supercomputers and AI.
Caltech researchers introduced a new more accurate, generalizable DL technique for solving PDEs, capable of solving entire families of PDEs—such as the Navier-Stokes equation—without needing retraining hoped to ease reliance on supercomputers increasing computational capacity to model bigger problems.
#NeuralNetworks (NNs) are usually trained to approximate #functions between inputs and outputs defined in #Euclidean #space, your classic graph with x, y, and z axes. But this time, the researchers decided to define the inputs and outputs in #Fourier #space, which is a special type of graph for plotting #wave #frequencies. The #intuition that they drew upon from work in other fields is that something like the motion of air can actually be described as a combination of wave frequencies. The general direction of the wind at a macro level is like a low frequency with very long, lethargic waves, while the little eddies that form at the micro level are like high frequencies with very short and rapid ones.
Why does this matter? Because it’s far easier to approximate a Fourier function in Fourier space than to wrangle with PDEs in Euclidean space, which greatly simplifies the NN’s job. Cue major accuracy and efficiency gains: in addition to huge speed advantage, their technique achieves a 30% lower error rate when solving Navier-Stokes than previous deep-learning methods.
United States Air Force Air Force Research Laboratory #AI #Quant #Cyber #Crypto #Quantum #Ventures: #ABMS2: Beyond #JADC2 to #JADAC2 & #JADCAC2: https://lnkd.in/ecpxbPi
AIMLExchange™: AIMLExchange.com: We create the Digital Future™
C4I-Cyber™: C4I-Cyber.com: Because the Future of the World Depends Upon It™
#MIT #ComputerScience & #AI #Lab: AI-ML-DL-NLP-RPA Guide: https://lnkd.in/eknKzm5:
#Princeton #AI #Cyber #Crypto #Quantum #Risk #Computing ModelRiskArbitrage.com:
Global Risk Management Network LLC: Silicon Valley-Wall Street-Pentagon-Worldwide Digital Pioneer
