@InProceedings{Zardian2026PhysicsInformedMachine, author = {Zardian, Mohsen Gol and Downey, Austin R.J. and Tronci, Eleonora Maria and Madden, Conor and Coble, Daniel and Navidi, Sina and Hu, Chao}, booktitle = {Data Science in Engineering, 2026, Vol. 9}, title = {Physics-Informed Machine Learning Part III: Hard-Constraint ODE Method for Structural Dynamics}, year = {2026}, pages = {49--60}, publisher = {River Publishers}, series = {IMAC XLIV}, collection = {IMAC XLIV}, doi = {10.13052/rp-9788743814207a06}, }