Expensive models and experiments
PIML can reduce repeated simulation or experimental cost while retaining the governing knowledge used in Artificial Intelligence and Machine Learning.
Engineering Research Community
Artificial Intelligence and Machine Learning & Physics-Informed Machine Learning
Physics-grounded modelling, learning and validation for Artificial Intelligence and Machine Learning
Artificial Intelligence and Machine Learning focuses on learning algorithms, representations, optimization, perception, reasoning and autonomous decision systems. Within PIML, the branch designs inductive biases that respect equations, symmetries, conservation, geometry, stability and causal structure.
Its distinctive contribution is algorithmic: deciding whether knowledge belongs in inputs, loss functions, architectures, differentiable simulators, operators or post-processing, and establishing when that choice improves sample efficiency and reliable generalization.
This page presents ten focused research areas, degree-level project pathways, selected publications and direct support through the PIMLS biweekly members meeting.
This Artificial Intelligence and Machine Learning guide covers Physics-Informed Neural Networks (PINNs), physics-guided machine learning, scientific machine learning, neural operators, hybrid models and engineering digital twins. Explore the research and project pathways below, then join the Physics-Informed Machine Learning Society to connect with the international PIMLS community.
The central ideaEstablished Artificial Intelligence and Machine Learning knowledge + measurements and simulation + machine learning
10focused research areas
3academic project pathways
6selected publications
Biweeklymember research meeting
Why this combination matters
Why Artificial Intelligence and Machine Learning Needs Physics-Informed Learning
Use available scientific knowledge to make limited data more useful, transparent and testable.
Incomplete engineering models
Learn uncertain parameters, closures or discrepancies around an inspectable mechanistic foundation.
Transfer across conditions
Test whether structured models generalize across geometries, materials, assets, operating regimes or sites.
Trustworthy evidence
Use physical residuals, independent measurements, uncertainty and conventional engineering baselines before deployment.
Ten focused directions
Major Artificial Intelligence and Machine Learning PIML Research Areas
Each card connects a meaningful Artificial Intelligence and Machine Learning question with suitable scientific knowledge, modelling choices and evidence needed to test it.
01
Physics-Informed Neural Networks
Differential-equation residuals supervise forward and inverse learning. PIML opportunities: Improve optimization, adaptive sampling, domain decomposition and error estimation.
Model and evidenceGoverning equations, calibrated measurements and held-out operating conditions
02
Neural ODEs and State-Space Models
Continuous-time latent dynamics support irregular observations and control. PIML opportunities: Encode stability, energy and known state transitions.
Model and evidenceMechanistic and data-only baselines, uncertainty and independent validation
03
Neural Operators
Operators learn solution maps over inputs, parameters and forcings. PIML opportunities: Develop geometry-aware, multi-scale and uncertainty-capable variants.
Model and evidenceGeometry, material or system parameters, sensor data and physical residuals
04
Equivariant Networks
Physical outputs transform predictably under rotations, translations or permutations. PIML opportunities: Build exact symmetries into representations and quantify data-efficiency benefits.
Model and evidenceGoverning equations, calibrated measurements and held-out operating conditions
05
Graph-Based Physical Learning
Meshes, molecules and networks have relational structure. PIML opportunities: Conserve fluxes/messages and generalize across topology and resolution.
Model and evidenceMechanistic and data-only baselines, uncertainty and independent validation
06
Differentiable Programming
Trainable pipelines can include solvers, filters and controllers. PIML opportunities: Study gradient accuracy, discontinuities, stiffness and memory cost.
Model and evidenceGeometry, material or system parameters, sensor data and physical residuals
07
Hybrid Residual Learning
A mechanistic model often has structured discrepancy. PIML opportunities: Learn bounded corrections with uncertainty rather than replacing the complete model.
Model and evidenceGoverning equations, calibrated measurements and held-out operating conditions
08
Equation and Constitutive Discovery
Unknown laws must be inferred without spurious terms. PIML opportunities: Combine sparsity, dimensional consistency, invariance and experiment design.
Model and evidenceMechanistic and data-only baselines, uncertainty and independent validation
09
Physics-Informed Reinforcement Learning
Exploration in physical systems can be unsafe and expensive. PIML opportunities: Use models, constraints and control-barrier concepts with offline and sim-to-real evaluation.
Model and evidenceGeometry, material or system parameters, sensor data and physical residuals
10
Generative Scientific AI
Generative models can propose fields, geometries and materials. PIML opportunities: Enforce feasibility and independently verify novelty, diversity and physical validity.
Model and evidenceGoverning equations, calibrated measurements and held-out operating conditions
Choose the right research depth
Projects for Every Academic Stage
Start with a scope that matches your time, mathematical background, experimental access and expected research contribution.
Project pathway 1
B.E./B.Tech
Learn the foundations with a bounded, measurable system.
- PINN optimizer comparison
- energy-preserving neural ODE
- equivariant network demonstration
- graph simulator with conservation checks
Expected outcome
A reproducible implementation, clear baselines, a manageable dataset and physically meaningful validation.
Project pathway 2
M.Tech
Combine an engineering model, substantial data and rigorous comparison.
- adaptive-domain PINN
- uncertainty-aware neural operator
- differentiable simulator calibration
- safe physics-informed RL benchmark
Expected outcome
A thesis-quality study with held-out regimes, mechanistic and data-only baselines, ablation and uncertainty.
Project pathway 3
Ph.D.
Address a publishable methodological, multiscale or deployment research gap.
- scalable multi-physics operator learning
- formal guarantees for hybrid learned dynamics
- foundation models for physical systems
- automated selection of physical inductive biases
Expected outcome
New methodology or validated engineering insight, multi-regime evidence, reproducible software and journal publications.
From idea to evidence
A Strong PIML Project Workflow
01
Define
Choose one Artificial Intelligence and Machine Learning question and a measurable engineering output.
02
Model
State the governing relationships, constraints or validated domain knowledge you will retain.
03
Compare
Build mechanistic and data-only baselines before the hybrid model.
04
Validate
Hold out experiments, conditions, assets, sites or regimes at the deployment level.
05
Publish
Report uncertainty, ablation, limitations, data lineage and reproducible code.
Read before you modelDiscuss Your Literature
Selected Publications and Why They Matter
Use this focused reading list to understand the general PIML framework, direct Artificial Intelligence and Machine Learning evidence and suitable hybrid modelling methods.
Literature review advice
Do not list papers only. Compare the engineering question, incorporated knowledge, data, split strategy, baselines, uncertainty and evidence level.
This source is included in the Artificial Intelligence and Machine Learning literature guide because it demonstrates or reviews a relevant physics-informed, hybrid, inverse, surrogate or scientific-machine-learning approach. Read the methods, data split, baselines and validation evidence—not only the reported accuracy.
How to use this paper: Use this paper to refine the research question, identify a defensible physical prior and compare evidence requirements for Artificial Intelligence and Machine Learning.
Read publication or record This source is included in the Artificial Intelligence and Machine Learning literature guide because it demonstrates or reviews a relevant physics-informed, hybrid, inverse, surrogate or scientific-machine-learning approach. Read the methods, data split, baselines and validation evidence—not only the reported accuracy.
How to use this paper: Use this paper to refine the research question, identify a defensible physical prior and compare evidence requirements for Artificial Intelligence and Machine Learning.
Read publication or record This source is included in the Artificial Intelligence and Machine Learning literature guide because it demonstrates or reviews a relevant physics-informed, hybrid, inverse, surrogate or scientific-machine-learning approach. Read the methods, data split, baselines and validation evidence—not only the reported accuracy.
How to use this paper: Use this paper to refine the research question, identify a defensible physical prior and compare evidence requirements for Artificial Intelligence and Machine Learning.
Read publication or record This source is included in the Artificial Intelligence and Machine Learning literature guide because it demonstrates or reviews a relevant physics-informed, hybrid, inverse, surrogate or scientific-machine-learning approach. Read the methods, data split, baselines and validation evidence—not only the reported accuracy.
How to use this paper: Use this paper to refine the research question, identify a defensible physical prior and compare evidence requirements for Artificial Intelligence and Machine Learning.
Read publication or record This source is included in the Artificial Intelligence and Machine Learning literature guide because it demonstrates or reviews a relevant physics-informed, hybrid, inverse, surrogate or scientific-machine-learning approach. Read the methods, data split, baselines and validation evidence—not only the reported accuracy.
How to use this paper: Use this paper to refine the research question, identify a defensible physical prior and compare evidence requirements for Artificial Intelligence and Machine Learning.
Read publication or record This source is included in the Artificial Intelligence and Machine Learning literature guide because it demonstrates or reviews a relevant physics-informed, hybrid, inverse, surrogate or scientific-machine-learning approach. Read the methods, data split, baselines and validation evidence—not only the reported accuracy.
How to use this paper: Use this paper to refine the research question, identify a defensible physical prior and compare evidence requirements for Artificial Intelligence and Machine Learning.
Read publication or record Build an interdisciplinary team
Where Artificial Intelligence and Machine Learning Can Collaborate
Computer Science
Scientific ML, optimization, trustworthy AI and reproducible research software.
Applied Mathematics
Differential equations, numerical methods, inverse problems and uncertainty.
Sensing & Control
Instrumentation, data acquisition, state estimation and responsible deployment.
Domain Laboratories
Experiments, calibration, validation evidence and practical expertise for Artificial Intelligence and Machine Learning.
Before you begin
Frequently Asked Research Questions
These answers help students avoid common scope, terminology and validation mistakes.
Still have a question?
Use the biweekly meeting form for research guidance.
Request accessNo. Artificial Intelligence and Machine Learning projects may use physics-guided features, hybrid residual models, differentiable simulators, neural operators, constrained architectures or data assimilation. State exactly what knowledge is incorporated.
Choose one engineering question, a measurable output and a defensible mechanistic baseline. Add learning only where data can identify an uncertainty or discrepancy.
A meaningful question, justified prior knowledge, deployment-level holdouts, strong baselines, ablation, uncertainty, reproducibility and honest limitations.
Simulation can broaden coverage, but simulation-only evidence cannot establish real-system accuracy. Use calibrated experiments, field measurements or trusted independent references appropriate to the claim.
Submit the biweekly members meeting form to discuss your project level, branch, data, model, validation plan and possible collaborators.
Take the next step
Bring your Artificial Intelligence and Machine Learning research idea to PIMLS
Join the biweekly members meeting for project guidance, collaboration and publication planning—or contact the Society directly.
Meeting participation is requested through the Google form. Complete it carefully so the Society can understand your research interest.