When I was in the first grade and just learning to read and write, I recall a page in our schoolbook that featured pictures of people in various occupations. The teacher asked us, “Which one would you like to become when you grow up?” Most of my classmates chose the usual answers, such as doctor, lawyer, engineer, or police officer. I was probably the only one who said, “I want to be the man digging underground for coal or gold, discovering precious stones and unseen things„. In the Romanian language, this job is called „miner”. The teacher smiled at my unusual answer.
If someone asked me the same question today, I would definitely not say „miner“ anymore. I would probably say, „I want to become a doctor in medicine„. Fun fact: while studying computer engineering for my bachelor’s degree, I also enrolled in a one-semester course in general medicine at UMFT (before this, I even check TU Wien, hearing from a friend that there go some of the best students to study medicine), as I was fascinated by how the human body works (and always knew, deep down, that I’m a doctor in a holistic sense). Later, I took another semester in nutrition and dietetics for the same reason at UMFT. Eventually, I had to give up medicine studies because the schedule left me with no free time at all to complete my bachelor in computer engineering; main reason: lectures at the medicine university started early in the morning and ended late in the evening due to free timeslots in between classes.
After finishing my master’s degree in applied informatics (specialization: web-design), I even thought about starting medicine again, this time in Heidelberg. A dear older female friend stopped me with one sentence I still remember clearly: „If you start medicine now, you’d probably be around forty by the time you finish specializing. It might be worth considering staying in IT and exploring more practical or hands-on paths there„. She was perhaps right at that time, and I didn’t attend, but it’s the only slight regret I have in life: that I didn’t pursue a career in medicine, so that I could practice as a doctor today. However, my curiosity for biology and medicine never really went away. It simply changed form: instead of becoming a medical doctor, I began exploring how computing could aid in understanding living systems.
When I first began working with physics-guided AI at the German Aerospace Center (DLR), I learned how adding physical knowledge to neural networks could make them safer and more sustainable. Later, at Chemnitz University of Technology, I worked on neuromorphic computing using printed memristors, where physical circuit laws guided the behavior of artificial neurons. These experiences shaped how I now think about AI: not as a closed box that fits data, but as something that can learn within the laws of nature.
Building on that perspective, and motivated by the challenge of working on something difficult in my free time, I developed my latest research paper, “Modeling Glucocorticoid-Induced Renin Regulation from Sparse Data Using Physics-Informed Neural Networks”, which was published today in AI in Medicine. You can find the supplementary experiments document here.
More exactly, this problem has been difficult to model quantitatively because the available data are extremely sparse. Traditional modeling methods depend on rich time-series measurements and clearly identifiable parameters. In this case, there were only a handful of data points and many unknowns, a situation most modelers would consider impossible. But that was precisely what drew me in a few years ago when I had my first discussion about it with Dr.med. Larissa Latia.
The medical challenge is real. More than 30% of patients treated with glucocorticoids develop hypertension, but we still cannot predict who will be affected or why. The underlying biochemical mechanism involves receptor binding, gene regulation, and hormone feedback, which are too difficult to estimate reliably with standard methods when the data are this limited. The data I used came from Dr.med. Larissa Latia’s 2020 doctoral work at Heinrich Heine University Düsseldorf, which provided the first systematic dose-response study of dexamethasone’s effects on renin secretion in As4.1 juxtaglomerular cells. The dataset was scientifically valuable but very small, comprising only four dexamethasone doses measured at a single 24-hour time point, resulting in a total of 36 data values. Each measurement captured only the final renin secretion level after 24 hours, not the intermediate molecular processes leading to it. Traditionally, such a dataset would be considered impossible to model. The system has around 11 biochemical parameters that act on different timescales, ranging from receptor binding, which takes minutes, to protein secretion, which takes hours or days. The parameter-to-data ratio is approximately 0.31, significantly below the threshold that conventional approaches can handle. When I tried a standard nonlinear ODE fit, it failed. The optimizer identified numerous mathematically feasible parameter sets, but none of them were biologically plausible. The resulting model even had a negative R² value, meaning it predicted worse than simply using the average.
To move forward, I turned to PINNs, which I discovered and worked with for the first time at the DLR, as I pointed earlier. These models combine the flexibility of neural networks with the structure of physical equations. Instead of fitting data points alone, the network must also satisfy the governing physical laws at many points across time. In this paper, those laws describe receptor-ligand interactions, transcriptional inhibition, mRNA turnover, and protein secretion. By enforcing these physical constraints, the model could make better use of the limited data. It effectively filled in the missing time dimension, ensuring consistency between the four doses even though the data existed only at one time point.
The key breakthrough came from systematic calibration. Instead of guessing how much to weight the data versus the physics, I explored a range of settings and discovered something unexpected. The best overall balance occurred at an intermediate weighting between data fit and mechanistic constraints. To ensure robustness, I also introduced an adaptive “plateau ramp” scheduling strategy to gradually increase the influence of the physics constraint during training. In supplementary ablation tests, the ramped strategy improved the plausibility pass rate from 50% to 90%, indicating substantially more stable training. In this regime, the model respected the physics sufficiently to remain biologically plausible, yet it remained flexible enough to follow the data where necessary.
At this optimal balance, the model achieved:
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R² = 0.803, compared to 0.759 for a conventional PINN and -0.220 for the ODE fit.
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The model also produced numerically much narrower spread than the ODE-only baseline, though this should not be interpreted as full biological identifiability. The estimated IC₅₀ was 2.925 ± 0.012 mg/dl and the Hill coefficient was 1.950 ± 0.009, both within about 1.6 percent of the expected biological targets used in the model.
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Furthermore, the residual diagnostics were broadly consistent with an adequate fit, including checks for normality and autocorrelation, although all such tests remain limited by the very small sample size. This methodological rigor resulted in Information Criteria (AIC/BIC) improvements of 77× and 5.9× over baselines, favoring the PINN over the ODE baseline even when accounting for complexity.
Trained only on 24-hour measurements, it inferred model-dependent 48-hour trajectories across the modeled compartments. It reconstructed a plausible time evolution of renin production, much like recreating a movie from a single frame. The model also captured the observed non-monotonic dose-response, where renin suppression peaks at medium doses but partially recovers at very high doses. This pattern is consistent with possible receptor saturation or compensatory feedback mechanisms that simpler models would miss.
To validate the framework, I compared it against two baselines: a traditional ODE fit and a pure neural network. The ODE-only approach failed to produce a meaningful fit (R² = -0.220). The pure neural network fit the training data extremely well (training R² ≈ 0.97) but showed much weaker held-out performance, with mean held-out RMSE = 0.114. The physics-informed model achieved the strongest overall fit to the full dataset (R² = 0.803, RMSE = 0.024) while maintaining biologically plausible parameter estimates. In strict leave-one-dose-out evaluation, however, held-out-dose prediction remained challenging, especially for the highest dose, highlighting the limits of generalization under such sparse observations.
The entire implementation can be found on my GitHub repo here.
PS. Only more recently, after completing the work described above, did I encounter the Ψ-NN (Physics Structure-Informed Neural Network) framework. What stood out to me immediately was that it pushed the same intellectual direction one step further: beyond fitting data under physical constraints, toward discovering compact internal structure in learned models themselves. Since then, I have extended this line through my own Ψ-family work, including the published Ψ-HDL and Ψ-xLSTM frameworks, as well as newer follow-up papers currently under review or in preparation this year. At the time I developed this biomedical PINN study, I did not yet know about Ψ-NNs. Looking back now, however, this newer research direction gives me a broader methodological lens for understanding why structure, constraints, and deployability matter so much in physics-guided AI.
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