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can a neural network learn to walk as a physical object in a physics simulation? here I train walking neural nets with an evolutionary algorithm. The input nodes/feet are activated by sine waves at learned phases & connections between two neurons extend based on their difference

Matt Henderson

80,126 subscribers

339,220 Aufrufe • vor 3 Jahren •via X (Twitter)

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10 Kommentare

Profilbild von Matt Henderson

Matt Hendersonvor 3 Jahren

aka “embodied neural networks”

Profilbild von Matt Henderson

Matt Hendersonvor 3 Jahren

Remember soda constructor?

Profilbild von Patrick Ꝺoyle

Patrick Ꝺoylevor 3 Jahren

Whatever the result, they seem to be enjoying themselves.

Profilbild von Eric Jang

Eric Jangvor 3 Jahren

this is amazing. would you consider open-sourcing the code? I'd love to extend this to optimizing the architecture of the net itself, so it ends up having to trade off physical bulk with function approximation power

Profilbild von Tom

Tomvor 3 Jahren

Looks kinda similar

Profilbild von Austen Lamacraft

Austen Lamacraftvor 3 Jahren

Surely a CNN will work better because of the strides?

Profilbild von c7ddfc

c7ddfcvor 3 Jahren

reminds me of this, also controlled by a neural net

Profilbild von Mike Vella

Mike Vellavor 3 Jahren

How do you think of this stuff??

Profilbild von Matt Henderson

Matt Hendersonvor 3 Jahren

I saw a cool demo of a neural net controlling an inverted pendulum, and was thinking it would be cool to make a nnet control something. I was also thinking about that old game soda constructor. Then I thought of this idea like a bad joke about learning to walk

Profilbild von Connor McCormick

Connor McCormickvor 3 Jahren

You should make it so that the ground is a treadmill with numbers on it, and the fitness function rewards it both for walking and for adding the numbers it's touching correctly.

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92,077 Aufrufe • vor 7 Monaten

What are Physics-Informed Neural Networks (PINNs) Physics-Informed Neural Networks (PINNs) are neural nets trained to satisfy a differential equation. The trick is simple. You bake the PDE residual straight into the loss. They came out of a very practical pain point. Classical PDE pipelines can be amazing, but they often demand a lot of setup work. Meshes. Stencils. Stability tuning. And once you build a solver, it’s usually tied to one geometry and one discretization choice. A PINN flips the workflow. You represent the solution itself as a smooth function uᵩ(x,t) and you enforce the physics wherever you choose to sample the domain. Most people first meet PINNs in the least helpful way. A pretty solution surface, almost no clarity on what was enforced to make it appear. In this series we keep the enforcement visible. We pick a PDE, represent the unknown solution as a flexible function, measure how badly that function violates the equation across the domain, and train it to reduce that mismatch at the points we sample. A normal neural net learns from labels. You give it inputs and target outputs. A PINN learns from an equation. You give it inputs (x,t), and it gets penalized whenever its output fails the PDE. Smaller mismatch means smaller loss. Bigger mismatch means bigger loss. That’s all “punish” and “reward” mean here. The network isn’t replacing physics. It’s just a flexible function that we force to obey the same calculus you’d demand from any candidate solution. The math breakdown: We start with a PDE 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 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’d have rᵩ(x,t) = 0 everywhere. We may also have data points (xᵢ,tᵢ,uᵢ) from measurements or from an initial condition. The training objective is 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 collocation points in Ω L_bc/ic(ᵩ) = penalties enforcing boundary conditions and initial conditions The key technical step is how we get the derivatives inside rᵩ. We don’t approximate them with finite differences. We compute them with automatic differentiation: ∂uᵩ/∂t, ∂uᵩ/∂x, ∂²uᵩ/∂x², … Then we differentiate the total loss L(ᵩ) with respect to ᵩ and train with gradient descent. That’s the whole idea. 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, with color showing 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 #ScientificMachineLearning #PDE #DifferentialEquations #Optimization #MachineLearning #AppliedMath #ComputationalPhysics

What are Physics-Informed Neural Networks (PINNs) Physics-Informed Neural Networks (PINNs) are neural nets trained to satisfy a differential equation. The trick is simple. You bake the PDE residual straight into the loss. They came out of a very practical pain point. Classical PDE pipelines can be amazing, but they often demand a lot of setup work. Meshes. Stencils. Stability tuning. And once you build a solver, it’s usually tied to one geometry and one discretization choice. A PINN flips the workflow. You represent the solution itself as a smooth function uᵩ(x,t) and you enforce the physics wherever you choose to sample the domain. Most people first meet PINNs in the least helpful way. A pretty solution surface, almost no clarity on what was enforced to make it appear. In this series we keep the enforcement visible. We pick a PDE, represent the unknown solution as a flexible function, measure how badly that function violates the equation across the domain, and train it to reduce that mismatch at the points we sample. A normal neural net learns from labels. You give it inputs and target outputs. A PINN learns from an equation. You give it inputs (x,t), and it gets penalized whenever its output fails the PDE. Smaller mismatch means smaller loss. Bigger mismatch means bigger loss. That’s all “punish” and “reward” mean here. The network isn’t replacing physics. It’s just a flexible function that we force to obey the same calculus you’d demand from any candidate solution. The math breakdown: We start with a PDE 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 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’d have rᵩ(x,t) = 0 everywhere. We may also have data points (xᵢ,tᵢ,uᵢ) from measurements or from an initial condition. The training objective is 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 collocation points in Ω L_bc/ic(ᵩ) = penalties enforcing boundary conditions and initial conditions The key technical step is how we get the derivatives inside rᵩ. We don’t approximate them with finite differences. We compute them with automatic differentiation: ∂uᵩ/∂t, ∂uᵩ/∂x, ∂²uᵩ/∂x², … Then we differentiate the total loss L(ᵩ) with respect to ᵩ and train with gradient descent. That’s the whole idea. 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, with color showing 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 #ScientificMachineLearning #PDE #DifferentialEquations #Optimization #MachineLearning #AppliedMath #ComputationalPhysics

Mathelirium

44,712 Aufrufe • vor 5 Monaten

Why is the Midjourney team uniquely qualified to build medical hardware? Beff (e/acc), founder of Extropic: "David's a trained physicist. He worked at NASA. He was a founder of Leap Motion, which is completely slept on as one of the first major projects he worked on." "What I really like about that team is that a lot of the same team from Leap Motion followed David into Midjourney and now into this hardware exploration." "They were training neural nets before there was TensorFlow, before there was GPUs. They did it on CPUs, and they had some of the first neural network technology deployed in a consumer product." "So people are like, 'Why would a gen AI company pivot into medical devices?' It's really folks that came from the hardware world finding this unique blend between neural nets and hardware to achieve things people didn't think were possible." "If it's physically possible, I very much have faith that that team can pull it off."

Why is the Midjourney team uniquely qualified to build medical hardware? Beff (e/acc), founder of Extropic: "David's a trained physicist. He worked at NASA. He was a founder of Leap Motion, which is completely slept on as one of the first major projects he worked on." "What I really like about that team is that a lot of the same team from Leap Motion followed David into Midjourney and now into this hardware exploration." "They were training neural nets before there was TensorFlow, before there was GPUs. They did it on CPUs, and they had some of the first neural network technology deployed in a consumer product." "So people are like, 'Why would a gen AI company pivot into medical devices?' It's really folks that came from the hardware world finding this unique blend between neural nets and hardware to achieve things people didn't think were possible." "If it's physically possible, I very much have faith that that team can pull it off."

MTS

62,195 Aufrufe • vor 25 Tagen