paper edits

paper/paper.md

@@ -49,7 +49,7 @@ The software allows users to supply the underlying PDE model, quantity of intere
 while providing implementations for commonly used risk measures, including expectation, variance, and superquantile/conditional-value-at-risk (CVaR).
 as well as derivative-based optimizers. 
 SOUPy leverages FEniCS [@LoggMardalWells12] for the formulation, discretization, and solution of PDEs, 
-and the framework of hIPPYlib [@VillaPetraGhattas18; @VillaPetraGhattas21] for sampling from random fields, adjoint-based and matrix-free derivative computation,
+and the framework of hIPPYlib [@VillaPetraGhattas18; @VillaPetraGhattas21] for sampling from random fields and adjoint-based derivative computation,
 while also providing interfaces to existing optimization algorithms in SciPy.
 
 
@@ -68,7 +68,7 @@ This results in a complex optimization problem in which each evaluation of the o
 
 SOUPy provides a platform to formulate and solve such PDE-constrained OUU problems using efficient derivative-based optimization methods. 
 Users supply the definitions for the PDE constraint, QoI, and additional penalization terms for the optimization variable, and are given the option to choose from a suite of used risk measures.
-At a core functionality, SOUPy implements sample-based evaluation of risk measures and their derivatives, where parallel-in-sample computation is supported through MPI. 
+As a core functionality, SOUPy implements sample-based evaluation of risk measures as well as their gradients and Hessians, where parallel-in-sample computation is supported through MPI. 
 The resulting cost functionals can then be minimized using SOUPy's implementations of large-scale optimization algorithms, such as L-BFGS [@LiuNocedal89] and Inexact Newton-CG [@EisenstatWalker96; @Steihaug83], 
 or through algorithms available in SciPy [@2020SciPy-NMeth] using the provided interface.