The foundations, literally.
Diploma and B.Tech in Civil Engineering at the Central Institute of Technology, Kokrajhar (9.2 & 8.98 CGPA). Concrete, surveying, structures — I learned how the physical world is held up, and where it fails.
01 — The Throughline
From concrete to computation.
I began by learning to build with concrete and steel in a small town in Assam. Somewhere along the way I fell for the equations underneath the structures — and then for teaching computers to solve them faster than we ever could by hand. This is that trajectory.
Falling for the mathematics.
M.Tech at IIT Madras — top 5% of my class (CGPA 9.22), GATE top 3% nationwide. Numerical methods, optimization, data science. I stopped seeing beams and started seeing boundary-value problems. My first PINNs paper for inverse problems in heterogeneous media.
Teaching operators to learn physics.
PhD in Civil & Systems Engineering with Dr. Somdatta Goswami. Deep operator networks that learn hidden physics to 95% accuracy, differentiable predictive control of PDEs, neural surrogates for traumatic-brain-injury modeling and fracture.
Scaling to the national labs.
Multi-GPU neural-operator training on Argonne's Polaris (two Director's Discretionary Awards, 5,600 node-hours; 83% faster). Chishiki AI Fellow at UT Austin. 1st place, global Tesseract differentiable-simulation hackathon.
Interfaces, at the Livermore scale.
Graduate research intern at the Data Science Institute — building agentic workflows for materials-science applications and geometry-aware neural operators for moving-interface problems.
02 — What I Work On
Four questions I keep chasing.
\(\mathcal{G}_\theta\)
Neural Operators
Learning maps between infinite-dimensional function spaces — \(\mathcal{G}_\theta : a(x)\!\mapsto\! u(x)\) — DeepONets and FNOs that replace expensive solvers and generalize across geometries and parameters.
DeepONet · FNO · JAX\(\min_{f} J\)
Differentiable PDE Control
Steering physical systems in real time. Differentiable predictive control with time-integrated operators, robust to noise, delay, and the sim-to-real gap.
DPC · MPC · Control\(\nabla_a\mathcal{L}\)
Inverse Problems & Hidden Physics
Recovering material properties and governing parameters from sparse, noisy data by minimizing \(\mathcal{L}=\lVert b - F(\hat a)\rVert^2\) with interface-aware networks.
PINNs · I-PINNs · Inversion\(\textstyle\sum_{\text{GPU}}\)
HPC & Scale
Distributed multi-GPU training of high-dimensional operators on leadership-class supercomputers — because physics doesn't fit on one card.
CUDA · MPI · Polaris
03 — The Live Lab
Simulations, running in your browser.
Every panel below integrates a real governing equation, live, on your device — no videos, no pre-baked frames. Drag the parameters and watch the physics respond. These interactive demos mirror the systems I accelerate with neural operators in my research (see the real results ↓).
Fig. 01 — Hyperbolic PDE
live
Wave Equation
\[ \frac{\partial^2 u}{\partial t^2} = c^2\nabla^2 u \;-\; \gamma\,\frac{\partial u}{\partial t} \]
A vibrating membrane integrated by explicit finite differences and rendered as a live 3D wireframe. A driven source ripples outward; the damping term \(\gamma\) bleeds energy away.
Fig. 02 — Phase field
live
Allen–Cahn Phase Separation
\[ \frac{\partial u}{\partial t} = \varepsilon^2\nabla^2 u + u - u^3 \]
Spinodal decomposition: a uniform mixture spontaneously separates into two phases and coarsens, minimizing interface energy. The same physics behind alloys, foams, and the moving interfaces I model at Livermore.
Fig. 03 — Incompressible flow
move / drag your cursor across the field
Turbulence & Smoke
\[ \frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u}\!\cdot\!\nabla)\mathbf{u} = -\nabla p + \nu\nabla^2\mathbf{u},\quad \nabla\!\cdot\!\mathbf{u}=0 \]
A genuine incompressible fluid solver (Stam's stable-fluids method): semi-Lagrangian advection, diffusion, and a pressure projection that keeps the flow divergence-free. Push it and watch vortices shed and tangle.
Fig. 04 — Feedback control
live
Learning to Control a PDE
\[ \frac{\partial u}{\partial t} = \alpha\,\frac{\partial^2 u}{\partial x^2} + f(x,t),\quad f = K\big(u^{*}(x,t)-u\big) \]
A heated rod that must track a moving target profile \(u^{*}\) (dashed). Distributed actuators inject and remove heat; a feedback policy drives the error to zero. A toy of my differentiable predictive control work — accepted at IEEE CDC 2026.
04 — Research in Motion
The real thing.
The interactive demos above are teaching tools. These are actual outputs from my papers — neural-operator controllers, learned surrogates, and high-fidelity solvers, straight from the experiments.
Uncontrolled
→
Controlled (DPC)
Stabilizing the European power grid after a fault
\( M_i\,\dot{\omega}_i = P_i - D_i\,\omega_i - \sum_j B_{ij}\sin(\delta_i-\delta_j),\quad \dot{\delta}_i=\omega_i \)
A 900 MW generation loss in Greece sends a frequency-deviation \(|\Delta f|\) wave across the continent. Left: uncontrolled, the disturbance propagates. Right: differentiable predictive control drives every node's frequency back to nominal in real time.
2D Navier–Stokes density transport
\( \partial_t \omega + (\mathbf{u}\!\cdot\!\nabla)\omega = \nu\nabla^2\omega \)
Cardinality-invariant neural-operator policies (CINOC) for multi-agent control of incompressible flow — scalable to any number of actuators and sensors. The differentiable-simulation pipeline that won 1st place at the global Tesseract hackathon.
Controlling a 1D reaction–diffusion front
\( \partial_t u = D\,\partial_{xx} u + r\,u(1-u) \)
Differentiable predictive control on a time-integrated neural operator drives the state \(u(x,t)\) to a target profile \(u^{*}\) with distributed actuators — accepted at IEEE CDC 2026.
Phase-field solidification
\( \partial_t \phi = -M\,\frac{\delta \mathcal{F}}{\delta \phi} \)
Dendritic microstructure growth — the class of geometry-aware moving-interface problems I build neural operators for at Lawrence Livermore.
Operator surrogate vs. the ground-truth solver
Across 3,000 unseen samples the time-integrated DeepONet matches the finite-difference solver to a median relative \(L_2\) error of 1.11% — while running orders of magnitude faster, which is what makes real-time control tractable.
05 — Selected Work
Where the equations meet the world.
Learning Hidden Physics & Parameters
Deep operator networks that recover governing parameters from data — \(\hat a \leftarrow \hat a - \gamma\nabla\mathcal{L}\) — to 95% accuracy. Published in CMAME.
CINOC — Cardinality-Invariant Operator Policies
Scalable PDE control policies invariant to the number of actuators and sensors. Accepted at ICML 2026.
Real-Time Traumatic Brain Injury Modeling
Multimodal neural operators for real-time TBI biomechanics — toward personalized protective-gear design. WSE Trainee Award finalist.
ARIA — AI Teaching Assistant
A multimodal RAG assistant for Statics & Mechanics, deployed to 90 students in production on Streamlit.
Scalable Multi-GPU Operator Training
Distributed CUDA + MPI training of high-dimensional PDE operators — 83% faster, 5,600 awarded node-hours on Polaris.
Hybrid Neural–FEM Fracture Simulation
A neural-operator + finite-element hybrid that accelerates crack propagation while preserving accuracy, with an RL agent steering the crack. Built with FEniCSx.
06 — Publications
The full list.
Every paper, preprint, and work in review — across ML venues, computational-mechanics journals, and controls conferences. Also on my Google Scholar.
- ICML 2026
CINOC: Cardinality-Invariant Neural Operator Policies for Scalable PDE Control
Zanotta P., Sarkar D.R., Zheng H., Goswami S., Drgoňa J.
- IEEE CDC 2026
Learning to Control PDEs with Differentiable Predictive Control and Time-Integrated Neural Operators
Sarkar D.R., Goswami S. · arXiv:2511.08992
- CMAME 2026
Learning Hidden Physics and System Parameters with Deep Operator Networks
Sarkar D.R., Kag V., Pal B., Goswami S. · 456:118926
- CMPB 2026
Multimodal Neural Operators for Real-Time Biomechanical Modelling of Traumatic Brain Injury
Agarwal A., Sarkar D.R., Goswami S. · 109398
- arXiv 2025
Learning Generalizable Neural Operators for Inverse Problems
Thorpe A.J., Tretiakov S., Sarkar D.R., Kumar K., Topcu U. · arXiv:2512.18120
- FEAD 2025
Adaptive Interface-PINNs for Inverse Problems: Determining Material Properties for Heterogeneous Systems
Sarkar D.R., Annavarapu C., Roy P. · 249:104373
- ESREL 2025
Uncertainty-Aware Optimization in Engineered Systems via Gradient Boosting and Differential Evolution
Sarkar D.R., Basu S., Manuel L., Goswami S.
- EDU · RAG
ARIA: Adaptive Retrieval Intelligence Assistant — A Multimodal RAG Framework for Engineering Education
Luo Y., Sarkar D.R., Sangree R.H., Goswami S. · arXiv:2604.06179
- FEAD 2025
Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: forward and inverse problems in heterogeneous media
Roy S., Sarkar D.R., Annavarapu C., Roy P., Lecampion B., Valiveti D.M. · 244:104305
- Under review
Interface Physics-Informed Neural Networks (I-PINNs) to Solve Inverse Problems in Heterogeneous Materials
Sarkar D.R., Annavarapu C., Roy P. · Machine Learning for Computational Science and Engineering
07 — Recognition
Some things that went right.
Chishiki AI Graduate FellowshipSCIPE · UT Austin · 2026–27
1st — Tesseract HackathonGlobal · differentiable simulation
2× Director's Discretionary AwardArgonne ALCF · 5,600 node-hours
3rd — NASA & DNV ChallengeOptimization under uncertainty
WSE Trainee Award FinalistTBI modeling · JHU 2025
Creel Family FellowshipJohns Hopkins · 2024–25
GATE 2022 · Top 3%96.96 percentile nationwide
TATA Motors Excellence ScholarshipAcademic performance
08 — Life Beyond the Solver
Conferences, labs, and the road.
Research is a team sport played across continents. A few frames from the journey — from an M.Tech convocation in Chennai to ICML and the Sierra granite behind Livermore.
09 — Let's build something
Working on operators, control, or SciML at scale?