Physics-Informed Neural Networks (PINNs) - An Introduction - Ben Moseley | Jousef Murad
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- Опубліковано 31 тра 2023
- 🌎 Website: jousefmurad.com
Physics-informed neural networks (PINNs) offer a new and versatile approach for solving scientific problems by combining deep learning with known physical laws. Such networks are able to simulate physical systems, invert for their underlying parameters and even discover underlying physical laws themselves. In this introductory workshop and live coding session we will cover the basic definition of a PINN, their pros and cons compared to traditional scientific techniques and some of the state-of-the-art research in the field.
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![Physics Informed Neural Networks (PINNs) [Physics Informed Machine Learning]](http://i.ytimg.com/vi/-zrY7P2dVC4/mqdefault.jpg)
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+1 for Oxford PhD saying "timesing" instead of multiplying... respect! :D
at 14:30, it seems like external force will not operate on Unn. External force will be a constant term in the physics loss function.
Thanks for sharing this recording from the workshop. Thanks, Ben!
I love all of the questions!! 🤓 Ben is a great teacher!
We are talking of relatively simple oscillator problem. How about if we have complex geometries for which FEM methods are most suited today? I have been reading of physics informed graph nets for the purpose of complex geomeries. Do you have any references for complex domains? Lets say i have a complex shaped mechanical component subjected to pressure fir which i normslly use FEM.?
Nice lesson and clear presentation. Thank you!
A great introduction and massive thanks for sharing the knowledge!
Fantastic introduction, much appreciated!
Very nice and clear presentation.
could you please provide the example code of PINN?. Link in the comments not working.
Great work!
great work
nice tutorial. thank you.
Great video on this fascinating field. Thanks for sharing.
Sure :)
Thank you for such an informative lecture on PINN.
Thanks for watching! :)
OMG, very cool video!!! The training performance is highly dependent on the "lambda" value, do you have ideas about how to define its value? Many thanks.
similar question as some others. When we are solving even standard physics electrostatics, heat transfer etc, forget time domain, so only elliptic equations on complex CAD, I am wondering what applications can PINNs be used for. as opposed to using FEM. maybe shape optimization type problems? or inverse problems?
A possibly useful method would be to have the neural network identify the invariants or a Lie group for a differential equation. Another approach, compute all scalar quantities and have neural network find the right combination of scalar quantities to find a Lagrangian for a physical system.
I wonder if this give better results with PDE for option pricing
code link where can I get?
well done,the trend information is also very important,and it can be involved by a partial differential equation.i think maybe the parameters of the partial differential equation can also be the parameters of the neural network PINNS
Thanks for PINN , is code available ?
I think MIT developed something related to this, not sure whether it is opensource
Great 👍
Sure :)
Very nice lesson! I'm stuck on the Task 3 though, I can't get the network to converge for w0=80. Here's the code if anyone can spot what I'm missing here:
torch.manual_seed(123)
# define a neural network to train
pinn = FCN(1,1,32,3)
# define additional a,b learnable parameters in the ansatz
# TODO: write code here
a = torch.nn.Parameter(torch.zeros(1, requires_grad=True))
b = torch.nn.Parameter(torch.zeros(1, requires_grad=True))
# define boundary points, for the boundary loss
t_boundary = torch.tensor(0.).view(-1,1).requires_grad_(True)
# define training points over the entire domain, for the physics loss
t_physics = torch.linspace(0,1,60).view(-1,1).requires_grad_(True)
# train the PINN
d, w0 = 2, 80# note w0 is higher!
mu, k = 2*d, w0**2
t_test = torch.linspace(0,1,300).view(-1,1)
u_exact = exact_solution(d, w0, t_test)
# add a,b to the optimiser
# TODO: write code here
optimiser = torch.optim.Adam(list(pinn.parameters())+[a]+[b],lr=1e-3)
for i in range(15001):
optimiser.zero_grad()
# compute each term of the PINN loss function above
# using the following hyperparameters:
lambda1, lambda2 = 1e-1, 1e-4
# compute boundary loss
# TODO: write code here (change to ansatz formulation)
u = pinn(t_boundary)*torch.sin(a*t_boundary+b)
loss1 = (torch.squeeze(u) - 1)**2
dudt = torch.autograd.grad(u, t_boundary, torch.ones_like(u), create_graph=True)[0]
loss2 = (torch.squeeze(dudt) - 0)**2
# compute physics loss
# TODO: write code here (change to ansatz formulation)
u = pinn(t_physics)*torch.sin(a*t_physics+b)
dudt = torch.autograd.grad(u, t_physics, torch.ones_like(u), create_graph=True)[0]
d2udt2 = torch.autograd.grad(dudt, t_physics, torch.ones_like(dudt), create_graph=True)[0]
loss3 = torch.mean((d2udt2 + mu*dudt + k*u)**2)
# backpropagate joint loss, take optimiser step
# TODO: write code here
loss = loss1 + lambda1*loss2 + lambda2*loss3
loss.backward()
optimiser.step()
# plot the result as training progresses
if i % 5000 == 0:
#print(u.abs().mean().item(), dudt.abs().mean().item(), d2udt2.abs().mean().item())
u = (pinn(t_test)*torch.sin(a*t_test+b)).detach()
plt.figure(figsize=(6,2.5))
plt.scatter(t_physics.detach()[:,0],
torch.zeros_like(t_physics)[:,0], s=20, lw=0, color="tab:green", alpha=0.6)
plt.scatter(t_boundary.detach()[:,0],
torch.zeros_like(t_boundary)[:,0], s=20, lw=0, color="tab:red", alpha=0.6)
plt.plot(t_test[:,0], u_exact[:,0], label="Exact solution", color="tab:grey", alpha=0.6)
plt.plot(t_test[:,0], u[:,0], label="PINN solution", color="tab:green")
plt.title(f"Training step {i}")
plt.legend()
plt.show()
Im a beginner in PyTorch and OpenFOAM since the last few years, but today i learned that my "dream" is called "PINN" 🙂