diff --git a/.github/workflows/Downgrade.yml b/.github/workflows/Downgrade.yml
new file mode 100644
index 0000000000..190d11e1f6
--- /dev/null
+++ b/.github/workflows/Downgrade.yml
@@ -0,0 +1,60 @@
+name: Downgrade
+on:
+  pull_request:
+    branches:
+      - master
+    paths-ignore:
+      - 'docs/**'
+  push:
+    branches:
+      - master
+    paths-ignore:
+      - 'docs/**'
+jobs:
+  test:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        group:
+          - QA
+          - ODEBPINN
+          - PDEBPINN
+          - NNPDE1
+          - NNPDE2
+          - AdaptiveLoss
+          - Logging
+          - Forward
+          - DGM
+        version:
+          - "1"
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v1
+        with:
+          version: ${{ matrix.version }}
+      - uses: actions/cache@v4
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - uses: julia-actions/julia-downgrade-compat@v1
+        with:
+          skip: LinearAlgebra, Pkg, Random, Test
+      - uses: julia-actions/julia-buildpkg@v1
+      - uses: julia-actions/julia-runtest@v1
+        env:
+          GROUP: ${{ matrix.group }}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: src,lib/NeuralPDELogging/src
+      - uses: codecov/codecov-action@v4
+        with:
+          files: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          fail_ci_if_error: true
diff --git a/Project.toml b/Project.toml
index 6545930693..d76565ff25 100644
--- a/Project.toml
+++ b/Project.toml
@@ -40,50 +40,50 @@ Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [compat]
 Adapt = "4"
-AdvancedHMC = "0.6"
+AdvancedHMC = "0.6.1"
 Aqua = "0.8"
-ArrayInterface = "7"
-CUDA = "5.1"
-ChainRulesCore = "1"
-ComponentArrays = "0.15"
+ArrayInterface = "7.7"
+CUDA = "5.2"
+ChainRulesCore = "1.18"
+ComponentArrays = "0.15.8"
 Cubature = "1.5"
-DiffEqBase = "6"
-DiffEqNoiseProcess = "5.1"
-Distributions = "0.25"
+DiffEqBase = "6.144"
+DiffEqNoiseProcess = "5.20"
+Distributions = "0.25.107"
 DocStringExtensions = "0.9"
 DomainSets = "0.6, 0.7"
-Flux = "0.14"
-ForwardDiff = "0.10"
-Functors = "0.4"
+Flux = "0.14.11"
+ForwardDiff = "0.10.36"
+Functors = "0.4.4"
 Integrals = "4"
 LineSearches = "7.2"
 LinearAlgebra = "1"
 LogDensityProblems = "2"
-Lux = "0.5"
-LuxCUDA = "0.3"
+Lux = "0.5.14"
+LuxCUDA = "0.3.2"
 MCMCChains = "6"
-ModelingToolkit = "8"
-MonteCarloMeasurements = "1"
+MethodOfLines = "0.10.7"
+ModelingToolkit = "8.75"
+MonteCarloMeasurements = "1.1"
 Optim = "1.7.8"
-Optimization = "3"
-OptimizationOptimJL = "0.2"
-OptimizationOptimisers = "0.2"
-OrdinaryDiffEq = "6"
+Optimization = "3.22"
+OptimizationOptimJL = "0.2.1"
+OptimizationOptimisers = "0.2.1"
+OrdinaryDiffEq = "6.70"
 Pkg = "1"
 QuasiMonteCarlo = "0.3.2"
 Random = "1"
-Reexport = "1.0"
-RuntimeGeneratedFunctions = "0.5"
+Reexport = "1.2"
+RuntimeGeneratedFunctions = "0.5.11"
 SafeTestsets = "0.1"
-SciMLBase = "2"
-Statistics = "1"
-SymbolicUtils = "1"
-Symbolics = "5"
+SciMLBase = "2.24"
+Statistics = "1.10"
+SymbolicUtils = "1.4"
+Symbolics = "5.17"
 Test = "1"
 UnPack = "1"
-Zygote = "0.6"
-MethodOfLines = "0.10.7"
-julia = "1.6"
+Zygote = "0.6.68"
+julia = "1.10"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
diff --git a/docs/make.jl b/docs/make.jl
index 3b1340c277..dfa8087f3f 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -13,7 +13,7 @@ makedocs(sitename = "NeuralPDE.jl",
          authors = "#",
          modules = [NeuralPDE],
          clean = true, doctest = false, linkcheck = true,
-         warnonly = [:missing_docs, :example_block],
+         warnonly = [:missing_docs],
          format = Documenter.HTML(assets = ["assets/favicon.ico"],
                                   canonical = "https://docs.sciml.ai/NeuralPDE/stable/"),
          pages = pages)
diff --git a/docs/src/tutorials/dgm.md b/docs/src/tutorials/dgm.md
index 1917df8f43..cb853d0099 100644
--- a/docs/src/tutorials/dgm.md
+++ b/docs/src/tutorials/dgm.md
@@ -28,15 +28,15 @@ where $\vec{x}$ is the concatenated vector of $(t, x)$ and $L$ is the number of
 
 Let's try to solve the following Burger's equation using Deep Galerkin Method for $\alpha = 0.05$ and compare our solution with the finite difference method:
 
-$$
+```math
 \partial_t u(t, x) + u(t, x) \partial_x u(t, x) - \alpha \partial_{xx} u(t, x) = 0 
-$$
+```
 
 defined over
 
-$$ 
+```math
 t \in [0, 1], x \in [-1, 1] 
-$$
+```
 
 with boundary conditions
 ```math
diff --git a/src/BPINN_ode.jl b/src/BPINN_ode.jl
index 4493a07326..3bbf1afea8 100644
--- a/src/BPINN_ode.jl
+++ b/src/BPINN_ode.jl
@@ -123,18 +123,19 @@ function BNNODE(chain, Kernel = HMC; strategy = nothing, draw_samples = 2000,
 end
 
 """
-Contains ahmc_bayesian_pinn_ode() function output:
-1> a MCMCChains.jl chain object for sampled parameters
-2> The set of all sampled parameters
-3> statistics like: 
-    > n_steps
-    > acceptance_rate
-    > log_density
-    > hamiltonian_energy
-    > hamiltonian_energy_error 
-    > numerical_error
-    > step_size
-    > nom_step_size
+Contains `ahmc_bayesian_pinn_ode()` function output:
+
+1. A MCMCChains.jl chain object for sampled parameters.
+2. The set of all sampled parameters.
+3. Statistics like:
+    - n_steps
+    - acceptance_rate
+    - log_density
+    - hamiltonian_energy
+    - hamiltonian_energy_error
+    - numerical_error
+    - step_size
+    - nom_step_size
 """
 struct BPINNstats{MC, S, ST}
     mcmc_chain::MC
@@ -143,10 +144,11 @@ struct BPINNstats{MC, S, ST}
 end
 
 """
-BPINN Solution contains the original solution from AdvancedHMC.jl sampling(BPINNstats contains fields related to that)
-> ensemblesol is the Probabilistic Estimate(MonteCarloMeasurements.jl Particles type) of Ensemble solution from All Neural Network's(made using all sampled parameters) output's.
-> estimated_nn_params - Probabilistic Estimate of NN params from sampled weights,biases
-> estimated_de_params - Probabilistic Estimate of DE params from sampled unknown DE parameters
+BPINN Solution contains the original solution from AdvancedHMC.jl sampling (BPINNstats contains fields related to that).
+
+1. `ensemblesol` is the Probabilistic Estimate (MonteCarloMeasurements.jl Particles type) of Ensemble solution from All Neural Network's (made using all sampled parameters) output's.
+2. `estimated_nn_params` - Probabilistic Estimate of NN params from sampled weights, biases.
+3. `estimated_de_params` - Probabilistic Estimate of DE params from sampled unknown DE parameters.
 """
 struct BPINNsolution{O <: BPINNstats, E, NP, OP, P}
     original::O
diff --git a/src/advancedHMC_MCMC.jl b/src/advancedHMC_MCMC.jl
index c051d208ca..6f30149257 100644
--- a/src/advancedHMC_MCMC.jl
+++ b/src/advancedHMC_MCMC.jl
@@ -344,8 +344,8 @@ end
 
 !!! warn
 
-    Note that ahmc_bayesian_pinn_ode() only supports ODEs which are written in the out-of-place form, i.e.
-    `du = f(u,p,t)`, and not `f(du,u,p,t)`. If not declared out-of-place, then the ahmc_bayesian_pinn_ode()
+    Note that `ahmc_bayesian_pinn_ode()` only supports ODEs which are written in the out-of-place form, i.e.
+    `du = f(u,p,t)`, and not `f(du,u,p,t)`. If not declared out-of-place, then the `ahmc_bayesian_pinn_ode()`
     will exit with an error.
 
 ## Example