He was a member of the U.S. Navy V-12 program at Iowa State College, and received his B.S. in aeronautical engineering there in 1946.[6] He earned his Ph.D. from the California Institute of Technology, graduating in 1951. His thesis An Interferometric Wind Tunnel Study of Transonic Flow past Wedge and Circular Arcs was advised by Hans W. Liepmann.
Bryson was the Ph.D. advisor to the Harvard control theorist Yu-Chi Ho.
In 1970, Bryson was elected a member of the National Academy of Engineering for contributions to engineering education and imaginative application of modern statistical methods to engineering optimization.
^Journal of Dynamic Systems, Measurement, and Control. American Society of Mechanical Engineers. 1981. p. 1967.
^Arthur E. Bryson (1961, April). A gradient method for optimizing multi-stage allocation processes. In Proceedings of the Harvard Univ. Symposium on digital computers and their applications.
^Stuart Dreyfus (1990). Artificial Neural Networks, Back Propagation and the Kelley-Bryson Gradient Procedure. J. Guidance, Control and Dynamics, 1990.
^Jürgen Schmidhuber (2015). Deep learning in neural networks: An overview. Neural Networks 61 (2015): 85-117. ArXiv