* chore: update to latest Lux

* test: run tests enabling type-instability checks

* chore: bump minimum versions

* adapt fix

* undo NNPDE_tests.jl

* Revert "adapt fix"

This reverts commit 71c7071.

* Array{eltypeθ}

* Revert "Array{eltypeθ}"

This reverts commit 6d6d670.

* convert

* add convert topost  adapt

* fix ε_

* fix

* fix convert

* update convert, adapt

* update project.toml

* update Project

* update Project

* update Project

* update

* fix

* typos

* fix: dependencies

* test: merge qa testing

* chore: run formatter

* fix: BPINN ODE testing

* fix: update minimum versions

* refactor: update DGM implementation

* test: mark weighted training test as broken

* refactor: remove junk boilerplate

* fix: element type handling

* fix: incorrect DGM architecture

* refactor: rearrange exports

* test: run logging with non-error depwarn

* fix: forward tests

* fix: downgrade testing

* refactor: cleanup NNODE

* refactor: use explicit imports

* refactor: cleanup NNDAE

* feat: bring back NNRODE

* refactor: cleanup PINN code

* fix: eltype conversions in IntegroDiff

* refactor: cleanup neural adapter code

* refactor: bayesian PINN ODEs

* fix: missing NNRODE tests

* fix: try fixing more tests

* fix: different device handling

* fix: Bayesian PINN

* test: try reducing maxiters

* refactor: more cleanup of neural adapter

* docs: update compat

* docs: cleanup

* refactor: cleanup of deps a bit

* fix: allow scalar for number types

* fix: neural adapter tests

* fix: final round of cleanup

* fix: remove incorrect NNRODE implementation

* refactor: remove NeuralPDELogging in-favor of extension (#901)

---------

Co-authored-by: KirillZubov <kirillzubov3@gmail.com>