[FEAT]: Add `NNStopping` #81

ashutosh-b-b · 2024-01-26T20:11:38Z

Checklist

Appropriate tests were added
Any code changes were done in a way that does not break public API
All documentation related to code changes were updated
The new code follows the
contributor guidelines, in particular the SciML Style Guide and
COLPRAC.
Any new documentation only uses public API

Additional context

Add any other context about the problem here.

Refactors old code from NeuralPDE

- adds test for a Bermudan max call example from paper - adds test for a Put Basket in Duprie's local volatility model

codecov · 2024-01-26T20:36:27Z

Codecov Report

Attention: 2 lines in your changes are missing coverage. Please review.

Comparison is base (3f1df12) 58.27% compared to head (66372d3) 63.06%.
Report is 8 commits behind head on main.

Files	Patch %	Lines
src/DeepBSDE.jl	0.00%	1 Missing ⚠️
src/DeepBSDE_Han.jl	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #81      +/-   ##
==========================================
+ Coverage   58.27%   63.06%   +4.78%     
==========================================
  Files           7        8       +1     
  Lines         580      647      +67     
==========================================
+ Hits          338      408      +70     
+ Misses        242      239       -3

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ChrisRackauckas · 2024-01-27T08:35:49Z

Missing docs

ChrisRackauckas · 2024-01-30T08:42:29Z

docs/src/tutorials/nnstopping.md

+```
+We then define a `SDEProblem`:
+```julia
+prob = SDEProblem(f, sigma, u0, tspan; payoff = g)


payoff isn't a valid kwarg here?

It is valid. We pick the payoff and redefine the SDEProblem to simulate:

HighDimPDE.jl/src/NNStopping.jl

Lines 26 to 28 in 2c516a3

g = prob.kwargs[:payoff]

sde_prob = SDEProblem(prob.f, prob.u0, prob.tspan)

No, that does not match the interface. We should throw an error in SciMLBase if that's done. I'll add that error soon to catch this better, but that means we need to make sure this satisfies a real interface. But since it's a package about solving PDEs, we should have the description in the PDE form.

In that case, I ll pick up the dispatch from the NNKolmogorov PR and put it here.

BTW, we can't simulate the SDE with this kwarg. But we can still construct it. The check should be at the construction level.

I added the dispatch : a935123
And updated NNStopping to work with it : 71fe64c

ChrisRackauckas · 2024-01-30T08:43:01Z

docs/src/NNStopping.md

+
+Similar to DeepSplitting and DeepBSDE, NNStopping evaluates the PDE as a Stochastic Differential Equation. Consider an Obstacle PDE of the form:
+```math
+ max\lbrace\partial_t u(t,x) + \mu(t, x) \nabla_x u(t,x) + \frac{1}{2} \sigma^2(t, x) \Delta_x u(t,x) , g(t,x) - u(t,x)\rbrace


Is this a PIDE?

Technically no. Its an obstacle PDE with non linear term f = 0:

I'm not sure I see a difference? It just requires f = 0. That can be checked.

Hm, I have a dispatch for f = 0 in the NNKolmogorov PR
:

HighDimPDE.jl/src/HighDimPDE.jl

Lines 126 to 134 in a158d47

function PIDEProblem(g,

μ,

σ,

tspan,

xspan;

p = nothing,

x0_sample = NoSampling(),

noise_rate_prototype = nothing,

kwargs...)

We can use that, with a kwarg for g. How does that sound?

This dipatch will cater to defining optimal stopping problems and kolmogorov PDE problems

ChrisRackauckas · 2024-02-01T01:19:12Z

src/HighDimPDE.jl

+* `xspan`: The domain of system state. This can be a tuple of floats for single dimension, and a vector of tuples for multiple dimensions. Where each tuple corresponds to a dimension of state vector.
+* `noise_rate_prototype` : Incase of a non diagonal noise, the prototype of `dx` in `σ`
+"""
+function PIDEProblem(μ,


why not just use nothing for f? I don't see why this would need another dispatch.

We donot need another one. But we need to change the existing one. The checks are hardcoded and always expect f ang g in a certain form.
I updated the only definition of PIDEProblem to accomodate defining all problems here: 901470e
Added some tests for PIDEProblem as well : 130cd20

ChrisRackauckas · 2024-02-01T17:03:56Z

docs/src/DeepSplitting.md

@@ -62,14 +62,14 @@ In `HighDimPDE.jl` the right parameter combination $\theta$ is found by iterativ
 `DeepSplitting` allows obtaining $u(t,x)$ on a single point  $x \in \Omega$ with the keyword $x$.

 ```julia
-prob = PIDEProblem(g, f, μ, σ, x, tspan)
+prob = PIDEProblem(μ, σ, x, tspan, g, f,)


this is a breaking change

Yes. We will need a breaking release. I'd suggest we do that after NNKolmogorov is in

ChrisRackauckas · 2024-02-01T19:00:04Z

src/HighDimPDE.jl

+    * f -> f(x, y, u(x, t), u(y, t), ∇u(x, t), ∇u(y, t), p, t)
+- Semilinear Parabolic Partial Differential Equation 
+    * f -> f(X, u, σᵀ∇u, p, t)


We should really just have one form?

Technically the equations are themselves different. And f means different things here.
For PIDEs (DeepSplitting and MLP) :

For DeepBSDE and DeepBSDE_Han :

We can consider naming them different. i.e. the integrated one f and the other one h

As discussed, I added a new problem : 518a2f1

ChrisRackauckas · 2024-02-01T19:00:17Z

src/HighDimPDE.jl

+    * f -> `nothing`
+    * x0 -> nothing, xspan must be provided.
+- Obstacle Partial Differential Equation 
+    * f -> `nothing`
+    * g -> `nothing`


If these can be nothing, make them kwargs?

These are now kwargs for ParabolicPDEProblem

ChrisRackauckas · 2024-02-01T19:00:29Z

src/HighDimPDE.jl

+* `x`: point where `u(x,t)` is approximated. Is required even in the case where `x0_sample` is provided. Determines the dimensionality of the PDE.
+* `tspan`: timespan of the problem.
+* `g` : initial condition, of the form `g(x, p, t)`.
+* `f` : when defining PIDE : nonlinear function, of the form `f(x, y, u(x, t), u(y, t), ∇u(x, t), ∇u(y, t), p, t)`. When defining Semilinear PDE: `f(X, u, σᵀ∇u, p, t)`


no, only one form. Multi-forms never work well.

This is resolved with the introduction of ParabolicPDEProblem

ChrisRackauckas · 2024-02-01T19:01:43Z

src/HighDimPDE.jl

+    * f -> `nothing`
+    * x0 -> nothing, xspan must be provided.
+- Obstacle Partial Differential Equation 
+    * f -> `nothing`


I don't think there's tests for f = nothing on the other methods.

There are f is nothing for Kolmogorov :

HighDimPDE.jl/test/PIDEProblem.jl

Line 142 in 32a66cc

@test prob.f == nothing

ashutosh-b-b · 2024-02-07T11:15:54Z

Updating for ParabolicPDEProblem:

518a2f1 : This separates PIDEProblem and a ParabolicPDEProblem.
ParabolicPDEProblem:

$$ \begin{aligned} (\partial_t u)(t,x) &= f\big(t,x, u(t,x), ( \nabla_x u )(t,x) \big) d{\bf x} + \big\langle \mu(t,x), ( \nabla_x u )( t,x ) \big\rangle + \tfrac{1}{2} \text{Trace} \big(\sigma(t,x) [ \sigma(t,x) ]^* ( \text{Hess}_x u)(t, x ) \big). \end{aligned} $$

# g(x) = u(T,x)
ParabolicPDEProblem(μ, σ, x0, tspan, g, f)
## When f = 0 for Kolmogorov Eqn , instead of x0 we have xspan where we sample multiple initial values. 
ParabolicPDEProblem(μ, σ, nothing, tspan, f; xspan)
## When f = 0 and instead of `g` we have `payoff` 
ParabolicPDEProblem(μ, σ, x0, tspan; payoff = payoff_func)

PIDEProblem:

$$ \begin{aligned} (\partial_t u)(t,x) &= \int_{\Omega} f\big(t,x,{\bf x}, u(t,x),u(t,{\bf x}), ( \nabla_x u )(t,x ),( \nabla_x u )(t,{\bf x} ) \big) d{\bf x} + \big\langle \mu(t,x), ( \nabla_x u )( t,x ) \big\rangle + \tfrac{1}{2} \text{Trace} \big(\sigma(t,x) [ \sigma(t,x) ]^* ( \text{Hess}_x u)(t, x ) \big). \end{aligned} $$

PIDEProblem(μ, σ, x0, tspan, g, f)

ChrisRackauckas · 2024-02-09T09:25:49Z

src/MLP.jl

-    g, f = prob.g, prob.f
+    g= prob.g 
+    f = if isa(prob, ParabolicPDEProblem)
+        (y, z, v_y, v_z, ∇v_y, ∇v_z, p, t) -> prob.f(y, v_y, ∇v_y, p, t )


it's not a direct translation like that though, since the interpretation of f is different?

It is, since here (for ParabolicPDEProblem) we are interested in non - integrating variables only. The integrating variables are z , v_z and ∇v_z.

Here's an example : Consider Earlier HighDimPDE.jl MLP

For Allen Cahn we had:

HighDimPDE.jl/test/MLP.jl

Lines 143 to 146 in e44771b

X0 = fill(0.0f0, d) # initial point

g(X) = 1.0f0 ./ (2.0f0 .+ 4.0f-1 * sum(X .^ 2)) # initial condition

a(u) = u - u^3

f(y, z, v_y, v_z, ∇v_y, ∇v_z, p, t) = -a.(v_y)

Notice that only v_y has been passed. That is how it is written for MLP. When the function is not integrated, pass only non-integrating values.

But how do you handle the local nonlinearity of the parabolic problem in a PIDEProblem?

If its a PIDEProblem : we mean to integrate f and we pass in the integrating vars, if its a PIDEProblem we donot integrate f we just pass in the non integrating vars. The anonymous function was added so as to not break things in MLP and DeepSplitting as much, since they already pass in variables as mentioned above. The always expect f to be (y, z, v_y, v_z, ∇v_y, ∇v_z, p, t) and expected the user to only pass non integrating vars incase of a ParabolicPDE. Which is not the case anymore since, the f for ParabolicPDEProblem has only non integrating vars

Where are the two forms written down?

Here are the docstrings specifying different forms:
For PIDEProblem :
https://github.com/ashutosh-b-b/HighDimPDE.jl/blob/9ba145589fa6766522f0d142686d2ac491fdb030/src/HighDimPDE.jl#L63

For ParabolicPDEProblem:
https://github.com/ashutosh-b-b/HighDimPDE.jl/blob/9ba145589fa6766522f0d142686d2ac491fdb030/src/HighDimPDE.jl#L151

Here's the MLP tutorial for reference: https://github.com/ashutosh-b-b/HighDimPDE.jl/blob/bb/nn_stopping/docs/src/tutorials/mlp.md

You don't write the PDE for the second one.

As in the docstring?

Added and updated docs here : 9534761 and here : a7358f7

docs/src/problems.md

ChrisRackauckas · 2024-02-09T13:40:20Z

The solvers should list which problems they support somewhere.

ashutosh-b-b · 2024-02-09T14:25:59Z

The solvers should list which problems they support somewhere.

I made the docstrings to show types now : 0f1c148
as well as added a section for problems supported for each solver:
66372d3

ashutosh-b-b and others added 9 commits January 23, 2024 16:00

feat: Add NNStopping for Optimal Stopping Problems

eea3b1f

test: add tests for NNStopping

cfd5b45

feat: add NNStopping for OptimalStopping Problem

2c516a3

Refactors old code from NeuralPDE

chore: export NNStopping

1fe1d3f

test: add tests for NNStopping

3faa879

- adds test for a Bermudan max call example from paper - adds test for a Put Basket in Duprie's local volatility model

docs: add docstring for NNStopping

d346a80

test: enable tests

f5c4fd5

chore: fix formatting

ab340cf

Merge branch 'main' into bb/nn_stopping

e0d07fb

ashutosh-b-b marked this pull request as ready for review January 26, 2024 20:15

ashutosh-b-b changed the title ~~Add NNStopping~~ [FEAT]: Add NNStopping Jan 27, 2024

ashutosh-b-b added 3 commits January 30, 2024 13:25

docs: add docs for NNStopping

e670a5a

docs: add tutorial for NNStopping

71ff37e

docs: add tutorial and page to pages.jl

de266d2

ChrisRackauckas reviewed Jan 30, 2024

View reviewed changes

ashutosh-b-b added 5 commits January 31, 2024 01:26

feat: add dispatch on PIDEProblem for non linear term 0

a935123

This dipatch will cater to defining optimal stopping problems and kolmogorov PDE problems

fix: update NNStopping to work with PIDEProblem

71fe64c

test: update tests

d9d9f4c

docs: update docs

425ab15

chore: fix formatting in pages.jl

0ada89c

ashutosh-b-b requested a review from ChrisRackauckas January 30, 2024 20:00

ashutosh-b-b added 3 commits January 31, 2024 01:31

docs: fix spelling errors

ab4be5a

test: update tests

31a64f1

test: Increase maxiters in DeepSplitting heat eqn tests

a698b96

ChrisRackauckas reviewed Feb 1, 2024

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ashutosh-b-b added 2 commits February 1, 2024 12:29

feat: update PIDEProblem definition to accomodate all kinds of equations

901470e

test: add tests for PIDEProblem

130cd20

ChrisRackauckas reviewed Feb 1, 2024

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ashutosh-b-b requested a review from ChrisRackauckas February 1, 2024 18:36

ChrisRackauckas reviewed Feb 1, 2024

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ashutosh-b-b requested a review from ChrisRackauckas February 1, 2024 19:23

sathvikbhagavan mentioned this pull request Feb 3, 2024

Issue with NNStopping Example code SciML/NeuralPDE.jl#680

Closed

ashutosh-b-b added 6 commits February 4, 2024 00:53

feat: add ParabolicPDEProblem

518a2f1

fix: update solve dispatches for ParabolicPDEProblem

dc66a82

test: update tests

ee934ad

test: make chain f64 in NNStopping tests

3fc048a

test: fix bug in runtests

ce172b4

test: increase error tolerance

9ba1455

ashutosh-b-b mentioned this pull request Feb 4, 2024

Add NNKolmogorov and NNParamKolmogorov #83

Merged

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ChrisRackauckas reviewed Feb 9, 2024

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ashutosh-b-b requested a review from ChrisRackauckas February 9, 2024 09:31

ashutosh-b-b added 3 commits February 9, 2024 15:25

docs: update docs for MLP and DeepSplitting

125182d

docs: add eqn for ParabolicPDEProblem

9534761

docs: add section on problems and add notes on defining problems

a7358f7

ChrisRackauckas reviewed Feb 9, 2024

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docs/src/problems.md Outdated Show resolved Hide resolved

Update docs/src/problems.md

53cc92b

ashutosh-b-b added 2 commits February 9, 2024 19:53

docs: make docstrings have TYPEDSIGNATURES

0f1c148

docs: explicilty add section for supported problems for each solver

66372d3

ashutosh-b-b requested a review from ChrisRackauckas February 9, 2024 15:04

ChrisRackauckas approved these changes Feb 9, 2024

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ChrisRackauckas merged commit ed7a4bf into SciML:main Feb 9, 2024
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	g = prob.kwargs[:payoff]

	sde_prob = SDEProblem(prob.f, prob.u0, prob.tspan)

	function PIDEProblem(g,
	μ,
	σ,
	tspan,
	xspan;
	p = nothing,
	x0_sample = NoSampling(),
	noise_rate_prototype = nothing,
	kwargs...)

	X0 = fill(0.0f0, d) # initial point
	g(X) = 1.0f0 ./ (2.0f0 .+ 4.0f-1 * sum(X .^ 2)) # initial condition
	a(u) = u - u^3
	f(y, z, v_y, v_z, ∇v_y, ∇v_z, p, t) = -a.(v_y)

[FEAT]: Add NNStopping #81

[FEAT]: Add NNStopping #81

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ashutosh-b-b commented Jan 26, 2024 • edited Loading

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ashutosh-b-b commented Feb 7, 2024

Updating for ParabolicPDEProblem:

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ChrisRackauckas commented Feb 9, 2024

ashutosh-b-b commented Feb 9, 2024

[FEAT]: Add `NNStopping` #81

[FEAT]: Add `NNStopping` #81

ashutosh-b-b commented Jan 26, 2024 •

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