An advanced electrodialysis process model in the Julia ecosystem

An advanced electrodialysis process model
in the Julia ecosystem

Bram De Jaegher, Ingmar Nopens

juliacon 2019

An advanced electrodialysis process model
in the Julia ecosystem

Bram De Jaegher, Ingmar Nopens

juliacon 2019

Electrodialysis removes charged components from liquids

Some charged components are annoying...

Modelling particle interactions is expensive

$ F_{p,i} = \sum{F_{p,j}} + F_{mem} + F_d \\ + F_{am} + F_h + F_l + F_e + ... $

→ need for an efficient description!

ODEs and neural networks made a baby...

Electric resistance is indicator of fouling

Let us test this on a simple example...

Cookbook for neural ODEs

Neural network/ML library
- ANN structure

ODE solvers

DataFrames, Plotting

							using Flux
							ann = Chain(Dense(4,8,σ), 
							    Dense(8,8,σ), 
							    Dense(8,8,σ), 
							    Dense(8,1)) 
							using DifferentialEquations, DiffEqFlux
							function dudt_(u::TrackedArray, p, t) 
								Flux.Tracker.collect([ann(u)[1])
							end
							prob = ODEProblem(dudt_, x, (t0, tend), p)
							using DataFrames, Plots, CSV

DiffEqFlux.jl – A Julia Library for Neural Differential Equations

Cookbook for neural ODEs

Neural network/ML library
- ANN structure

ODE solvers

DataFrames, Plotting

							using Flux
							ann = Chain(Dense(4,8,σ), 
							    Dense(8,8,σ), 
							    Dense(8,8,σ), 
							    Dense(8,1)) 
							using DifferentialEquations, DiffEqFlux
							function dudt_(u::TrackedArray, p, t) 
								Flux.Tracker.collect([ann(u)[1])
							end
							prob = ODEProblem(dudt_, x, (t0, tend), p)
							using DataFrames, Plots, CSV

DiffEqFlux.jl – A Julia Library for Neural Differential Equations

Cookbook for neural ODEs

Neural network/ML library
- ANN structure

ODE solvers

DataFrames, Plotting

							using Flux
							ann = Chain(Dense(4,8,σ), 
							    Dense(8,8,σ), 
							    Dense(8,8,σ), 
							    Dense(8,1)) 
							using DifferentialEquations, DiffEqFlux
							function dudt_(u::TrackedArray, p, t) 
								Flux.Tracker.collect([ann(u)[1])
							end
							prob = ODEProblem(dudt_, x, (t0, tend), p)
							using DataFrames, Plots, CSV