
Cross-Country Macroeconomic Forecasting Using Physics-Informed Neural Networks and Universal Differential Equations in Julia
Vrishank Sai Anand, Prathamesh Dinesh Joshi, Rajat Dandekar, Raj Dandekar, Sreedath Panat
Work on impactful SciML research projects. Present at top-tier venues. Convert projects into publications. Build physics-grounded ML models using Julia and the SciML ecosystem.
Instructors from
SciML research from our cohorts has been accepted, presented, and archived across leading venues in machine learning, scientific computing, and applied AI.






















Physics-Informed AI and SciML are shifting from academic papers to foundational infrastructure for engineering and science. Here is why the 2024-2026 window matters.
Projected ML market by 2030, up from ~$55-75B in 2024 (CAGR above 30%), with SciML emerging as a key industrial segment.
Market Research ›Standardized SciML infrastructure for Physics-Informed Neural Networks and neural operators, accelerating industrial adoption.
NVIDIA ›SciML models embed conservation laws and physical constraints directly, cutting data requirements drastically versus traditional ML.
Physics-Informed Neural Networks ›Companies like Amazon and Microsoft have dedicated AI-for-Science divisions, and firms such as HCLTech are actively hiring specialists in PINNs and SciML.
View HCLTech PINN Role ›From modeling pandemics to discovering equations, SciML enables research-grade applications across every scientific domain.





We teach three interconnected frameworks that form the foundation of modern Scientific ML. Each represents a different way to combine physics with neural networks, from embedding constraints in loss functions to replacing unknowns in differential equations.
The overarching paradigm that integrates domain knowledge with data-driven learning. SciML models achieve great forecasting with just 20% of the data traditional ML requires, because they leverage structural knowledge from physics, biology, and engineering.
PINNs embed differential equations, conservation laws, and boundary conditions directly into the neural network's loss function. The network learns to satisfy both the data and the governing physics simultaneously, producing solutions that are physically consistent by construction.
Neural ODEs replace ODE right-hand sides with neural networks for fully data-driven dynamics. UDEs go further: they keep known physics terms intact while using neural networks only for unknown components, enabling symbolic recovery of closed-form equations.
Julia's composable ecosystem (DifferentialEquations.jl, Lux.jl, Optimization.jl) integrates ODE solvers and neural networks seamlessly. Julia is as fast as C, as readable as Python, and has native support for automatic differentiation.
Unlike black-box ML, SciML produces models grounded in physical laws. After training, use symbolic regression to recover closed-form equations from neural networks, achieving full interpretability of learned dynamics.
Apply these frameworks to computational physics, ecology, economics, health, fluid dynamics, climate science, and more. Any domain with partially known governing equations benefits from this hybrid approach.
Publication-quality diagrams illustrating the core frameworks you will master in this bootcamp.
Input data flows through three complementary frameworks: Physics-Informed Neural Networks embed constraints in loss functions, Neural ODEs learn continuous dynamics, and Universal Differential Equations combine known physics with neural networks for unknown terms.

The UDE training pipeline: known physics is preserved while neural networks approximate unknown dynamics. The ODE solver produces predictions, the loss function compares against data, adjoint methods compute gradients, and symbolic regression recovers closed-form equations.

A neural network takes spatiotemporal coordinates as input and outputs the solution. Three weighted loss terms enforce data fidelity, PDE residuals, and boundary/initial conditions, ensuring physically consistent predictions.

Whether you come from physics, engineering, economics, or biology, this bootcamp teaches you to integrate machine learning with your existing domain expertise.
PhD students and postdocs who want to apply ML to their domain (physics, biology, chemistry, ecology) while preserving theoretical rigor.
Mechanical, chemical, civil, and aerospace engineers looking to augment traditional simulation methods with data-driven hybrid approaches.
ML practitioners who want to move beyond black-box models and build physics-constrained systems that generalize better with less data.
Economists, biologists, climate scientists, and other domain specialists looking to incorporate ML into their mathematical models.
15 topics spanning Julia programming, ODE/PDE modeling, PINNs, Neural ODEs, UDEs, and hands-on research projects aimed at publication.
Led by Dr. Raj Dandekar
Led by Dr. Raj Dandekar
Led by Dr. Raj Dandekar
Led by Dr. Raj Dandekar
Led by Dr. Raj Dandekar
Led by Dr. Raj Dandekar
Led by Dr. Raj Dandekar
Led by Dr. Raj Dandekar
Led by Dr. Raj Dandekar
Led by Dr. Raj Dandekar
Led by Dr. Raj Dandekar
Led by Dr. Raj Dandekar
Led by Dr. Raj Dandekar
Led by Dr. Raj Dandekar
Led by Dr. Sreedath Panat
Everything you need to go from SciML beginner to publishing research-quality results in your domain.
Production-ready Julia code for every session, including PINNs, Neural ODEs, UDEs, and research projects.
Lifetime access to all session recordings and comprehensive lecture notes covering every SciML concept.
Two complete research projects (COVID-19 modeling and black hole dynamics) ready for your portfolio or publication.
Join the Vizuara SciML community on Discord for ongoing collaboration, doubt clearance, and research partnerships.
Our instructors are co-founders of Vizuara AI Labs and published researchers in Scientific Machine Learning, with expertise spanning physics-informed methods, neural differential equations, and applied ML.

Co-founder, Vizuara AI Labs
PhD from MIT, B.Tech from IIT Madras. Dr. Raj specializes in building LLMs from scratch, including DeepSeek-style architectures. His expertise spans AI agents, scientific machine learning, and end-to-end model development.

Co-founder, Vizuara AI Labs
PhD from Purdue University, B.Tech and M.Tech from IIT Madras. Dr. Rajat brings deep expertise in reinforcement learning and reasoning models, focusing on advanced AI techniques for real-world applications.

Co-founder, Vizuara AI Labs
PhD from MIT, B.Tech from IIT Madras. 10+ years of research experience. Dr. Panat brings deep technical expertise from both academia and industry to make complex AI concepts accessible and practical.

Manning #1 Best-Seller
Build a DeepSeek Model (From Scratch)
By Dr. Raj Dandekar, Dr. Rajat Dandekar, Dr. Sreedath Panat & Naman Dwivedi
Our lead instructor Dr. Raj Dandekar holds a PhD from MIT, where he conducted research at the Julia Lab under Prof. Alan Edelman and Chris Rackauckas, the creators of the SciML ecosystem.

A few recent SciML papers from our research over the past years. Students in the Researcher and Industry Professional plans work on similar projects aimed at publication.
Milestones, acceptances, and moments shared by Vizuara students and alumni on LinkedIn.
GVV Satyanarayana Raju
ex Chief Project Manager · IIIT Hyderabad
Kavya Subramanian
Boston University
Choose the plan that matches your goals, from self-paced learning to intensive research mentorship with MIT PhDs.
Save 43%. Originally Rs 30,000.
Save 38%. Originally Rs 60,000.
Save 24%. Originally Rs 1,25,000. Publish a paper in SciML with MIT and Purdue PhDs.
Save 20%. Originally Rs 1,50,000. MIT and Purdue PhDs as your industry advisors.
Everything you need to know about the SciML Research Bootcamp.
Join hundreds of researchers and engineers who have transformed their work with Scientific Machine Learning. Start building models that respect known science while discovering the unknown.
Reach out to our team on email for any questions about the bootcamp, curriculum, or application process.
research@vizuara.com
If the email discussion goes well and we find the candidate genuinely interested in research, we also provide a 1-on-1 15-minute talk with our Lead AI Scientist, Prathamesh Joshi.
Prathamesh Joshi
Lead AI Scientist · Vizuara AI Labs
Prathamesh Joshi is a Lead AI Scientist at Vizuara AI Labs, with prior experience at the Max Planck Institute, Germany. His expertise spans Generative AI and Scientific Machine Learning, with a strong publication record across ICLR Workshops, IEEE conferences, and other top venues. He has also mentored students through intensive bootcamps, guiding them toward publications at NeurIPS Workshops, ICLR, JuliaCon, and AAAI Workshops.