Preface to the column on "Aircraft Multidisciplinary Optimization Design Technology Based on Adjoint Theory"

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The aerodynamic configuration of an aircraft determines its shape and directly influences flight performance, platform functionality, and mission effectiveness. In modern aircraft development, increasing performance demands and technical complexity cause tighter disciplinary coupling, forcing configuration design to consider deeper interactions and pursue more integrated collaboration. Multidisciplinary integrated optimization based on numerical simulation and design theory enhances design and analysis capabilities and is a core technology for complex systems. NASA's CFD2030 Vision lists aircraft multidisciplinary design optimization (MDO) as one of six key technology directions. Traditional global and intelligent optimization methods suffer from exponential growth in data sampling and optimization time with design variables—the "curse of dimensionality". Conventional gradient-based methods scale linearly, but gradient evaluation remains inefficient. Gradient information indicates the direction of fastest function growth and is key to overcoming the curse of dimensionality; aerodynamic gradients point to the optimal evolution of the configuration. Thus, gradient-driven optimization is a key direction in the AIAA MDO framework. Efficient and accurate gradient computation is central to high-performance aerodynamic integrated optimization. The adjoint equation method, introduced from control theory by Professor Jameson in the 1990s, is an advanced gradient evaluation approach. By constructing and solving multidisciplinary coupled adjoint equations, it rapidly computes gradients of various objective functions with respect to design variables. The computational cost is independent of the number of design variables, offering high efficiency and serving as a core MDO technology. It has become an important research direction worldwide. After two decades, adjoint optimization has achieved substantial progress in aerodynamic optimization, low-boom design, aerodynamic-stealth integration, and blended-wing-body design, significantly improving aircraft performance and efficiency. Most leading aerodynamic software companies and research institutions actively develop adjoint platforms. Major commercial solvers like ANSYS Fluent and STAR-CCM+ have introduced adjoint capabilities. NASA Langley built a discrete adjoint platform based on FUN3D; DLR developed platforms based on Flower and TAU; ONERA based on elsA; Google built JAX-CFD using deep neural networks and automatic differentiation; Stanford's SU2 is an open-source adjoint platform; University of Michigan's ADFlow and OpenMDO enable aerodynamic-structural adjoint optimization. In China, Tsinghua University, Northwestern Polytechnical University, Nanjing University of Aeronautics and Astronautics, and China Aerodynamics Research and Development Center have actively explored adjoint theory, achieving advances in single-discipline and multidisciplinary coupled adjoint (aerodynamics, structures, internal flow, sonic boom, electromagnetics) and full-process adjoint optimization. China's aircraft aerodynamic configuration design is transitioning to digital optimization. Compared with international advanced levels, China's multidisciplinary coupling design platforms still face challenges: insufficient innovation in fundamental theoretical methods, heavy reliance on foreign open-source codes, and a gap with industrial design requirements. As performance requirements become more stringent, the demand for optimization efficiency and engineering applicability grows. Existing adjoint systems have considerable room for improvement in mechanism discovery, computational stability, and design efficiency. Several trends are emerging: First, establishing a cross-disciplinary unified theoretical framework, moving from single-discipline to multi-physics coupling, enabling efficient derivative transfer across aerodynamics, structures, thermal, acoustics, and electromagnetics, and developing a unified adjoint optimization framework for multi-physics, multi-configuration, and multi-mission scenarios. Second, advancing the engineering development of autonomous and controllable platforms, strengthening toolchain construction, enhancing scalability and integrability with computer-aided design/computer-aided engineering and model-based systems engineering. Third, fostering innovative integration with intelligent algorithms such as generative design, building design systems for conceptual, detailed, and agile design, thereby comprehensively improving design iteration efficiency. To showcase new theories, methods, and developments in this field, and to promote the continued progress and engineering translation of multidisciplinary coupled adjoint optimization, this special column presents "Technology for Aircraft Multidisciplinary Design Optimization Based on the Adjoint Method". It collects representative papers covering adjoint optimization methods, drag reduction design, low-boom configuration design and optimization, and aerodynamic-stealth adjoint optimization. The papers span theoretical modeling, numerical implementation, multidisciplinary coupling, and engineering applications, systematically presenting the latest research achievements and development trends. They offer strong theoretical and engineering practical value, serving as a reference for researchers, engineering designers, and graduate students. The successful completion of this special column would not have been possible without the authors' in-depth research, the expert reviewers' meticulous reviews, and the editorial team's diligent work. We extend our sincere gratitude to all.

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