TAEYEON is journeying into the World of Frozen for the first time in forever✨! Let’s follow in her footsteps and take a magical peek at Arendelle’s majestic fjord, traditional architecture, and iconic spots📍! Let’s go together “Into the Unknown!” #TAEYEON# #태연# #GirlsGeneration# #소녀시대# #LetItGo# #WorldOfFrozen# #HKDisneyland# #魔雪奇緣世界# #香港迪士尼樂園#

DIAMOND HANDS. We’re about to blast through the atmosphere and leave gravity in the dust! Ready to venture into the unknown? Strap in tight. Rockets don’t have brakes! 🚀

🎶 Come Let It Go at World of Frozen with the icon TAEYEON 🌬️!✨ K-pop Voice Queen TAEYEON is not only a big fan of “Frozen", but also the vocalist for the Korean version of “Into the Unknown,” the iconic hit song from “Frozen 2”🎶! Now she has answered her own call to adventure by visiting the world's first and largest “Frozen” themed land, exploring infinite possibilities in World of Frozen. Join her journey as she heads “Into the Unknown” to discover a world that’s both warmly familiar and unlike anything she has ever seen. 🏰 #TAEYEON# #태연# #GirlsGeneration# #소녀시대# #LetItGo# #WorldOfFrozen# #HKDisneyland# #魔雪奇緣世界# #香港迪士尼樂園#

What if Your Neural Network Was Forced to Obey Physics? Physics-Informed Neural Networks (PINNs) are neural networks trained to satisfy a differential equation by building the PDE residual directly into the loss. They emerged from a very practical problem...classical PDE pipelines can be brilliant, but they often demand heavy discretization work (meshes, stencils, stability tuning), and the method you build is usually tied to one geometry and one solver setup. A PINN flips the workflow by representing the solution itself as a smooth function uᵩ(x,t) and enforcing the physics everywhere you choose to sample the domain. People often meet PINNs in the least helpful way...via a flashy solution plot, and almost no explanation of what was enforced to get it. In this series we keep the enforcement visible. We pick a differential equation, represent the unknown solution as a flexible function, measure how well that function satisfies the equation across the domain, and train it to reduce that mismatch everywhere we sample. A normal neural net learns from labels...you give it inputs and target outputs. A PINN learns from a differential equation...you give it inputs (x,t) and it gets punished whenever its output fails the PDE. By punish we mean that the loss increases when the mismatch is large we reward it if the loss decreases as the mismatch gets smaller. The network isn’t replacing physics, it’s becoming a flexible function that is forced to satisfy the same calculus you’d impose on any candidate solution. The math breakdown: We start with a PDE we want to solve on a domain Ω. Write it as uₜ(x,t) + N(u(x,t), uₓ(x,t), uₓₓ(x,t), …) = 0 for (x,t) in Ω A PINN replaces the unknown function u with a neural network output uᵩ(x,t) Now define the physics residual by plugging uᵩ into the PDE rᵩ(x,t) = ∂uᵩ/∂t + N(uᵩ, ∂uᵩ/∂x, ∂²uᵩ/∂x², …) If uᵩ were an exact solution, we would have rᵩ(x,t) = 0 everywhere. We may also have data points (xᵢ,tᵢ,uᵢ) from measurements or a known initial condition. The training objective is just a weighted sum of squared errors L(ᵩ) = L_data(ᵩ) + λ L_phys(ᵩ) + L_bc/ic(ᵩ) with L_data(ᵩ) = meanᵢ |uᵩ(xᵢ,tᵢ) − uᵢ|² L_phys(ᵩ) = meanⱼ |rᵩ(xⱼ,tⱼ)|² where (xⱼ,tⱼ) are the collocation points in Ω L_bc/ic(ᵩ) = penalties enforcing boundary conditions and initial conditions The key technical step is that the derivatives inside rᵩ are computed by automatic differentiation ∂uᵩ/∂t, ∂uᵩ/∂x, ∂²uᵩ/∂x², … So we can differentiate the total loss L(ᵩ) with respect to ᵩ and train with gradient descent. This is the whole idea behind PINNs. Learn a function, but make the PDE part of the loss, so the network is trained to be a solution, not just a curve-fitter. In the render, the main 3D surface is the network’s current guess uᵩ(x,t), drawn as a living sheet over the (x,t) plane. Hovering above is the neural scaffold...a visible graph of feature nodes and connections. The bright tension threads are the physics residual rᵩ(x,t): each thread tethers a collocation bead on the sheet up to the scaffold, and it thickens and brightens exactly where |rᵩ| is large (color encodes the sign). As training runs, those threads go slack across the domain not because we hid the error, but because the network has actually been pushed toward rᵩ(x,t) ≈ 0. #PINNs# #PhysicsInformedNeuralNetworks# #ScientificMachineLearning# #PDE# #DifferentialEquations# #Optimization# #MachineLearning# #AppliedMath# #ComputationalPhysics#

Post 79 – What Truly is the Will of God? The world is racing into the great unknown, accelerating toward the space age. But never forget: there is a Creator behind that vast universe, and that Creator is God. God declared at Jesus baptism: “This is my beloved Son, in whom I am…

1/ An investigation into the opaque private loans/OTC, unilateral vesting changes, market maker coordination, unknown float, and >95% supply control behind $LAB's recent pump to $6B FDV. Here's why @LABtrade_ represents everything wrong with the current meta of retail extraction on major centralized exchanges.

1047 Games, the studio behind Splitgate, is working on a spiritual successor to Titanfall internally codenamed Empulse. >Team Deathmatch gameplay with grappling hooks, wall running, and boost pads for fast map traversal. >Giant mechs scattered around the maps that players can hop into. The one shown looked strikingly similar to Titanfall mechs. >The featured mech had a Gatling gun, deployable shield, and a missile launcher on cooldown. >Mech variety is still unknown. The project is still in very early pre-alpha, so everything is subject to change. It will be officially announced later this year.

Subnautica 2 launched into Early Access on Steam today and reached a peak of 457,897 concurrent players within the first hour. The underwater survival sequel from Unknown Worlds adds up to 4-player co-op and cross-play support. It launched with more than 5 million wishlists on the platform. The game is a major hit. Congrats to the devs

Looking at Earth being the perfect wonder among the stars, I really do think humanity belongs out there and needs to explore. Because who knows what else we will find? To a future where we become an interstellar civilization. I am so grateful to this killer crew: @satofishi Being an excellent mission commander and extraordinary space visionary, looking after us as a crew and caring for us. I will be forever grateful for letting us share this dream and challenging everyone around to think big and go forward in the very true spirit of the original Fram. @astro_jannicke Rocking it as a badass vehicle commander and filming star - always approachable. @Icetrek Space bestie and impressive human all around - the best person to teach one about pioneering, exploring and navigating unknowns. It impressed me how many people at @SpaceX have put their hearts and souls into making a powerful rocket launch a small metal tin out of this world, have it resist the vacuum of space and fall back through the atmosphere. If this isn't hardcore engineering, then what is? Also thank you to our trainers, medical team and support team, who transformed us from insecure novices to laid-back spacefarers. We owe our perceived coolness to you. And a special thanks to both the research and ham radio team at SpaceX for sharing all the nerdy joy. In general it was so inspiring to feel that everyone was living the attitude of: How does one make the impossible possible? Keep pushing boundaries, people!