Our researchers have developed a novel Monte Carlo method for computing derivatives of partial differential equation (PDE) solutions with respect to problem parameters. Key features include: ✅ Arbitrary point evaluation without global solve or mesh construction ✅ Ideal for inverse problems with complex geometries ✅ Easily parallelizable and agnostic to boundary representation ✅ Focuses on screened Poisson equations for diverse applications This method enables: 📐 PDE-constrained shape optimization 📊 Joint estimation of derivatives for all parameters ⚡ Fast, stable convergence in stochastic gradient-based optimization 🌡️ Applications span thermal design, shape from diffusion, and computer graphics. And, the approach promises significant advancements in scientific and geometric computing. Read the paper shared at #SIGGRAPHAsia2024 ➡️ https://nvda.ws/3ZBzQsq #NVIDIAResearch
This approach to computing derivatives in PDE solutions offers significant improvements in efficiency and accuracy. The focus on fast, stable convergence for stochastic gradient-based optimization is a critical step forward for diverse applications in thermal design and more.
To any engineer or applied mathematician who wants to save time on reading the paper: They tested a meshless method for solving linear elliptic PDEs using Monte Carlo methods. Make of it what you will, and no this summary was not AI generated.
That can be used for trade risk analysis as well. Because Monte Carlo simulations is a primary algorithm for risk analysis in various tradings.
Very informative
Interesting
Interesting
Now that is pretty darn cool
Interesting
Consultant in Patent Intelligence and Engineering Management
14hNVIDIA AI Monte Carlo (MC) method was from the Manhattan project in WWII for atomic bomb design. This concept of using math models to describe and simulate a physical process later became a weapon system called C4ISR, and now is called AI. There had been extensive nuclear tests to validate and verify (V&V) the math models and simulation results. But there is NO V&V effort on AI. This is very dangerous. Fast technology was also developed to facilitate MC simulation in the same project. AI is a sector needs fast computers. Why don't we use AI? Because it can't solve our problem. Do you or any of your contacts need our expertise and intellectual property (IP), a copyrighted Chinese-English multilingual metadata, to do the data analysis that AI can't do? NO one in the world can change the fact that we need menu to order our food at a restaurant. A five-year-old kid knows this. Similarly, we need metadata to search/retrieve the right data for data analytics. Metadata is a copyrighted content, NOT technology. It is fundamental to enable data analytics. Without metadata, NO data can be found/retrieved, even by the most advanced technologies, like AI. https://lnkd.in/g-aJFnXR