Merge pull request #581 from ChrisRackauckas-Claude/docs-improvements-20260107-120242

Documentation improvements: Fix grammar and clarity issues

Author: ChrisRackauckas

docs/src/basis.md

@@ -6,7 +6,7 @@ Basis
 
 ## API
 
-Next to [ModelingToolkits API](https://docs.sciml.ai/ModelingToolkit/stable/basics/AbstractSystem/) for `AbstractSystems`, a [`Basis`](@ref) can be called with the following methods:
+Next to [ModelingToolkit's API](https://docs.sciml.ai/ModelingToolkit/stable/basics/AbstractSystem/) for `AbstractSystems`, a [`Basis`](@ref) can be called with the following methods:
 
 ```@docs
 dynamics

docs/src/citations.md

@@ -4,7 +4,7 @@ If you are using `DataDrivenDiffEq.jl` for research, please cite
 
 ```bibtex
 @software{datadrivendiffeq,
-  author       = {JuliusMartensen and
+  author       = {Julius Martensen and
                   Christopher Rackauckas and others},
   title        = {DataDrivenDiffEq.jl},
   month        = jul,

docs/src/index.md

@@ -99,10 +99,10 @@ Pkg.add("DataDrivenSR")
 
   - See the [SciML Style Guide](https://github.com/SciML/SciMLStyle) for common coding practices and other style decisions.
   - There are a few community forums:
-    
+
       + The #diffeq-bridged and #sciml-bridged channels in the
-        [Julia Slack](https://julialang.org/slack/),
-        you can message @AlCap23 to start a discussion.
+        [Julia Slack](https://julialang.org/slack/).
+        You can message @AlCap23 to start a discussion.
       + The #diffeq-bridged and #sciml-bridged channels in the
         [Julia Zulip](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
       + On the [Julia Discourse forums](https://discourse.julialang.org)

docs/src/libs/datadrivensparse/sparse_regression.md

@@ -43,8 +43,8 @@ can be solved using an [`ImplicitOptimizer`](@ref). Similar to the formulation a
 Where the matrix of evaluated basis elements $\varPhi_y \in \mathbb R^{\lvert \varphi \rvert} \times \mathbb R^{m}$ now may also contain basis functions which are dependent on the target variables $y \in \mathbb R^{n_y}$.
 
 !!! warning "Tuning parameters for sparse regression"
-    
-    The algorithms used by `DataDrivenSparse` are sensible to the tuning of the hyperparameters! These are problem and coefficient specific, e.g. depend on the data and the unknown equations. While the examples used here are designed to work well, the used settings are not guaranteed to lead to success on other problems. User who want to explore the space of possible hyperparameters further might be interested in using [Hyperopt.jl](https://github.com/baggepinnen/Hyperopt.jl).
+
+    The algorithms used by `DataDrivenSparse` are sensitive to the tuning of the hyperparameters! These are problem and coefficient specific, e.g., depend on the data and the unknown equations. While the examples used here are designed to work well, the used settings are not guaranteed to lead to success on other problems. Users who want to explore the space of possible hyperparameters further might be interested in using [Hyperopt.jl](https://github.com/baggepinnen/Hyperopt.jl).
 
 ## [Algorithms](@id sparse_algorithms)
 

docs/src/solvers/common.md

@@ -59,4 +59,4 @@ Common choices for `selector` are `rss`, `bic`, `aic`, `aicc`, and `r2`. Given t
 options = DataDrivenCommonOptions(selector = (x) -> rss(x) / nobs(x))
 ```
 
-Which results in the mean squared error of the system.
+which results in the mean squared error of the system.