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Mathematical modeling in systems toxicology enables a comprehensive understanding of the effects of pharmaceutical substances on cardiac health.
Description and use of lsode, the livermore solver for ordinary differential equations
Radhakrishnan, K. and Hindmarsh, A. C · 1993
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A simple two-variable model of cardiac excitation
Aliev, R. R. and Panfilov, A. V · 1996
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Antiarrhythmic drugs and cardiac ion channels: mechanisms of action
Carmeliet, E. and Mubagwa, K · 1998
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channel blockers: potential antiarrhythmic agents
Gerlach, U · 2001
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Ionic mechanisms of electrophysiological properties and repolarization abnormalities in rabbit purkinje fibers
Corrias, A., Giles, W., and Rodriguez, B · 2011
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Adam: A method for stochastic optimization
Kingma, D. P. and Ba, J · 2014
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A web portal for in-silico action potential predictions
Williams, G. and Mirams, G. R · 2015
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Ha, D., Dai, A., and Le, Q. V · 2016
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An introduction to computational modeling of cardiac electrophysiology and arrhythmogenicity
Mayourian, J., Sobie, E. A., and Costa, K. D · 2018
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Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences
Alber, M., Buganza Tepole, A., Cannon, W. R., De, S., Dura-Bernal, S., Garikipati, K., Karniadakis, G., Lytton, W. W., Perdikaris, P., Petzold, L., et al · 2019
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Computational determination of herg-related cardiotoxicity of drug candidates
Lee, H.-M., Yu, M.-S., Kazmi, S. R., Oh, S. Y., Rhee, K.-H., Bae, M.-A., Lee, B. H., Shin, D.-S., Oh, K.-S., Ceong, H., et al · 2019
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Raissi, M., Perdikaris, P., and Karniadakis, G. E · 2019
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A practical guide to secondary pharmacology in drug discovery
Jenkinson, S., Schmidt, F., Ribeiro, L. R., Delaunois, A., and Valentin, J.-P · 2020
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Physics-informed neural networks for cardiac activation mapping
Sahli Costabal, F., Yang, Y., Perdikaris, P., Hurtado, D. E., and Kuhl, E · 2020
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Systems biology informed deep learning for inferring parameters and hidden dynamics
Yazdani, A., Lu, L., Raissi, M., and Karniadakis, G. E · 2020
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Cardiac transmembrane ion channels and action potentials: cellular physiology and arrhythmogenic behavior
András, V., Tomek, J., Nagy, N., Virág, L., Passini, E., Rodriguez, B., and Baczkó, I · 2021
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Hyperpinn: Learning parameterized differential equations with physics-informed hypernetworks
de Avila Belbute-Peres, F., Chen, Y.-f., and Sha, F · 2021
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Learning atrial fiber orientations and conductivity tensors from intracardiac maps using physics-informed neural networks
Grandits, T., Pezzuto, S., Costabal, F. S., Perdikaris, P., Pock, T., Plank, G., and Krause, R · 2021
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Systems biology: Identifiability analysis and parameter identification via systems-biology-informed neural networks
Daneker, M., Zhang, Z., Karniadakis, G. E., and Lu, L · 2023
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A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks
Wu, C., Zhu, M., Tan, Q., Kartha, Y., and Lu, L · 2023
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Learning the hodgkin–huxley model with operator learning techniques
Centofanti, E., Ghiotto, M., and Pavarino, L. F · 2024
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A brief review of hypernetworks in deep learning
Chauhan, V. K., Zhou, J., Lu, P., Molaei, S., and Clifton, D. A · 2024
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Chiu, C.-E., Pinto, A. L., Chowdhury, R. A., Christensen, K., and Varela, M · 2024
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Stiff-pinn: Physics-informed neural network for stiff chemical kinetics
Ji, W., Qiu, W., Shi, Z., Pan, S., and Deng, S · 2021
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Characterizing possible failure modes in physics-informed neural networks
Krishnapriyan, A., Gholami, A., Zhe, S., et al · 2021
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Systems biology informed neural networks (sbinn) predict response and novel combinations for pd-1 checkpoint blockade
Przedborski, M., Smalley, M., Thiyagarajan, S., Goldman, A., and Kohandel, M · 2021
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Scientific machine learning through physics-informed neural networks: Where we are and what’s next
Cuomo, S., Di Cola, V., Giampaolo, F., and Rozza, G · 2022
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Ep-pinns: Cardiac electrophysiology characterisation using physics-informed neural networks
Herrero Martin, C., Oved, A., Chowdhury, R. A., Ullmann, E., Peters, N. S., Bharath, A. A., and Varela, M · 2022
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Bayesian physics informed neural networks for real-world nonlinear dynamical systems
Linka, K., Schäfer, A., Meng, X., Zou, Z., Karniadakis, G. E., and Kuhl, E · 2022
Cited alongside, same era.
Accurate in silico simulation of the rabbit purkinje fiber electrophysiological assay to facilitate early pharmaceutical cardiosafety assessment: Dream or reality?
Mohr, M., Chambard, J.-M., Ballet, V., and Schmidt, F · 2022
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jinns: a jax library for physics-informed neural networks
Gangloff, H. and Jouvin, N · 2024
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An operator learning perspective on parameter-to-observable maps
Huang, D. Z., Nelsen, N. H., and Trautner, M · 2024
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A new method to compute the blood flow equations using the physics-informed neural operator
Li, L., Tai, X.-C., and Chan, R. H.-F · 2024
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Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation
Trayanova, N. A., Lyon, A., Shade, J., and Heijman, J · 2024
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Multi-objective loss balancing for physics-informed deep learning
Bischof, R. and Kraus, M. A · 2025
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Physics-informed neural networks with adaptive loss weighting algorithm for solving partial differential equations
Gao, B., Yao, R., and Li, Y · 2025
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Learning high-dimensional ionic model dynamics using fourier neural operators
Pellegrini, L., Ghiotto, M., Centofanti, E., and Pavarino, L. F · 2025
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