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Physics informed activation functions and loss functions for signal reconstruction and digital twinning

Year: 2026
Type: article
Abstract: A coupled two-body mass Lagrangian is used to model a magnetic rail nScrypt printer extruder with a sensor attached to the side for signal reconstruction and digital twinning. The equations of motion (EQM) derived from the Lagrangian are then used to improve the accelerometer signal by incorporating them as activation functions in the layers of the neural network, then using the damping constant and frequency matrix as learnable parameters. This is compared to a modular neural network that uses the EQM as the loss residuals for backward propagation and the physical constants as neural nets, both methods were found to give a root-mean square error (RMSE) of ~ 14 mm to 0.75 mm from the original position signal respectively. The physics informed neural network (PINN) activation layer produced a better detailed fit, while the PINN loss function produced a better average line and standard deviation. The two methods are then combined to achieve a final result with an RMSE of 0.96 mm to 16.7 mm, and a standard deviation that drops significantly during training to ~ 1.6 mm, but comparable to the PINN activation of 44-827 mm for test samples.
DOI: 10.1038/s41598-026-52773-4
Authors: Brent Cook, Adryel Gainza, Bryan Portocarrero, Mubarak Mujawar, Vivek Kamat, Dan Ewing, Himanshu Upadhyay, Shekhar Bhansali
Language: English
Open Access status: gold
Estimated APC paid: $2,690
Award: FLORIDA INTERNATIONAL UNIVERSITY ADVANCED SENSORS TECHNOLOGIES FOR APPLICATIONS IN ELECTRICAL ENGINEERING - RESEARCH AND INNOVATION EXCELLENCE CONSORTIUM (ASTERIX) ASTERIX CONSORTIUM AIMS TO ADDRESS THE NATION’S DIRE NEED FOR INCREASING THE PARTICIPATION OF UNDERREPRESENTED STUDENTS IN THE STEM WORKFORCE. THE CONSORTIUM INCLUDES INVESTIGATORS FROM FLORIDA INTERNATIONAL UNIVERSITY (FIU) - THE LARGEST HISPANIC SERVING INSTITUTION IN THE STATE OF FLORIDA, FLORIDA AGRICULTURAL AND MECHANICAL UNIVERSITY (FAMU) – THE ONLY HISTORICALLY BLACK INSTITUTION IN THE STATE OF FLORIDA, AND MIAMI-DADE COLLEGE – THE LARGEST HISPANIC SERVING COMMUNITY COLLEGE IN THE STATE OF FLORIDA. THE ASTERIX CONSORTIUM WILL BUILD A SUSTAINABLE PIPELINE OF TALENTED DIVERSE ENGINEERING STUDENTS WHO ARE HIGHLY PREPARED TO ENTER THE STEM WORKFORCE, ESPECIALLY IN AREAS OF INTEREST TO THE DEPARTMENT OF ENERGY/NATIONAL NUCLEAR SECURITY ADMINISTRATION (DOE/NNSA) ENTERPRISE. THE CONSORTIUM WILL LEVERAGE THE STRENGTHS OF EACH PARTNER INSTITUTION AND THE ESTABLISHED RESEARCH CONNECTIONS WITH DOE/NNSA INDUSTRY PARTNERS TO RECRUIT AND TRAIN ACADEMICALLY TALENTED K-20 MINORITY STUDENTS USING A VARIETY OF ACTIVITIES IN OUTREACH, EDUCATION AND RESEARCH. FURTHERMORE, THE FIU-FAMU-MDC ALLIANCE WILL SERVE ONE OF THE LARGEST POPULATIONS OF HISPANIC AND AFRICAN-AMERICAN STUDENTS IN THE NATION AND WILL CREATE INNOVATIVE ACADEMIC AND CAREER PATHWAYS FOR MINORITIES WHO WANT TO PURSUE ENGINEERING CAREERS. IN PARTICULAR THE CONSORTIUM WILL (A) RECRUIT WELL-QUALIFIED STEM STUDENTS TO SATISFY THE INCREASING DEMAND OF SCIENTISTS AND ENGINEERS IN AREAS OF INTEREST TO THE DOE, SPECIFICALLY IN ADVANCED SENSOR TECHNOLOGIES FOR VARIOUS APPLICATIONS IN ELECTRICAL ENGINEERING; (B) TRAIN STUDENTS IN UNDERGRADUATE AND GRADUATE RESEARCH AND PROVIDE ENRICHING EDUCATIONAL EXPERIENCES INCLUDING INTERNSHIP OPPORTUNITIES AT ASTERIX AND DOE LABORATORIES AND ENTERPRISES; (C) ATTRACT TALENTED UNDERREPRESENTED K-12 STUDENTS TO STEM DISCIPLINES THROUGH STRUCTURED OUTREACH ACTIVITIES AND EDUCATIONAL ENRICHMENT; AND (D) STRENGTHEN PARTNERSHIPS BETWEEN THE FIU, FAMU, AND MDC ELECTRICAL ENGINEERING DEPARTMENTS AND DOE ENTERPRISES TO TRAIN A CADRE OF SCIENTISTS AND ENGINEERS IN RESEARCH AREAS OF INTEREST TO DOE/NNSA.
OpenAlex ID: W7162185500
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Cites: 25
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