The paper introduces a graph-based methodology for constructing computational models that automates adjoint-based sensitivity analysis, particularly for large-scale multidisciplinary design optimization (MDO). The proposed method involves a three-stage compiler and a new modeling language called the Computational System Design Language (CSDL). This approach uses a graph representation of the numerical model to automatically generate a computational model that efficiently computes adjoint-based sensitivities. The methodology reduces the amount of user code by about two-thirds compared to traditional implementations without increasing computation time. The paper also includes a best-case complexity analysis to estimate memory requirements for evaluating computational models and their derivatives, independent of the compiler back end. Future implementations are expected to improve run-time performance and approach the theoretical best-case memory cost. The introduction discusses the limitations of general-purpose languages (GPLs) and software libraries in expressing domain-specific constructs, highlighting the advantages of domain-specific languages (DSLs) and algebraic modeling languages (AMLs) for optimization problems. The paper reviews various methods for derivative computation, including numerical differentiation, exact methods, and automatic differentiation (AD), and emphasizes the benefits of AD in terms of efficiency and automation.The paper introduces a graph-based methodology for constructing computational models that automates adjoint-based sensitivity analysis, particularly for large-scale multidisciplinary design optimization (MDO). The proposed method involves a three-stage compiler and a new modeling language called the Computational System Design Language (CSDL). This approach uses a graph representation of the numerical model to automatically generate a computational model that efficiently computes adjoint-based sensitivities. The methodology reduces the amount of user code by about two-thirds compared to traditional implementations without increasing computation time. The paper also includes a best-case complexity analysis to estimate memory requirements for evaluating computational models and their derivatives, independent of the compiler back end. Future implementations are expected to improve run-time performance and approach the theoretical best-case memory cost. The introduction discusses the limitations of general-purpose languages (GPLs) and software libraries in expressing domain-specific constructs, highlighting the advantages of domain-specific languages (DSLs) and algebraic modeling languages (AMLs) for optimization problems. The paper reviews various methods for derivative computation, including numerical differentiation, exact methods, and automatic differentiation (AD), and emphasizes the benefits of AD in terms of efficiency and automation.