New Research — MW Framework

Think Manifolds,
Not PDEs

339 Years After Newton's Principia Mathematica

Bayesian Cybersecurity introduces the Modak-Walawalkar Framework — a revolutionary physics-AI path that bypasses partial differential equations entirely. Where advanced mathematics meets practical threat detection.

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Newton and Principia Mathematica — 339 Years Later

Featured Research — March 2026

339 Years Later: A Physics-AI Path Alternative to Solving PDEs — Modak-Walawalkar Framework

PyTorch Pyro VAE Open Source

The 340-Year Pipeline

The Way Physics Has Always Been Done

Since Newton's Principia Mathematica (1687), every physics problem has followed the same pipeline. The MW Framework proposes a fundamentally different path.

1687

Newton's Principia

Forces & geometry applied explicitly to every body. F = ma for all.

1788

Lagrangian Mechanics

Lagrange replaced forces with a single energy function L. Universal procedure, same pipeline.

20th C

Supercomputers

Faster calculations — Maxwell, Navier-Stokes, Schrödinger, Einstein. Still deriving PDEs first.

2026

MW Framework

Think Manifolds, Not PDEs. A new way to think and a new way to solve. No derivation required.

The Old Pipeline vs. the New Path

Same Physics. Revolutionary Entry Point.

Real World Problem

Battery, fluid, signal...

→

Lagrangian

Energy function

→

Derive PDEs

Tensor calculus required

→

Solve PDEs

Supercomputers

↓ The MW Framework skips straight to:

Bayesian Priors

Domain knowledge

→

Train VAE

Learn the manifold

→

Read Residuals

Physics insights emerge

→

Millisecond Inference

No re-solving needed

The MW Framework

How It Works — Three Steps

Replace PDE derivation with Bayesian priors. Let the VAE discover the physics. Read the residuals to find what your theory missed.

Encode Your Physics as Bayesian Priors

Instead of deriving equations, you express what you know about your system as probability distributions. No tensor calculus. Just domain knowledge.

# Battery system priors — 3 lines, no PDEs
SOC ~ Beta(α, β)           # 0 to 1
current ≤ I_max via Normal  # physical limits
degradation monotonic       # only gets worse
                

Train a VAE to Learn the Manifold

A Variational Autoencoder (VAE) in PyTorch + Pyro takes your data and priors, learning the curved surface of physically possible states. No PDE written. No PDE solved.

# Standard PyTorch/Pyro training loop
model = PhysicsVAE(priors=battery_priors)
train(model, data, epochs=100)
# The manifold emerges from data + priors
# Equations are outputs, not inputs
                

Read the Residuals — Find What You Missed

Where the learned surface fits well, your physics is correct. Large residuals reveal exactly which assumption failed and by how much. The data pushes back against your theory.

SOC residual:         0.02  ✅ confirmed
current residual:     0.03  ✅ confirmed
degradation residual: 0.41  ⚠️ anomaly
→ something is regenerating charge
→ suspect lithium plating
                

The Physics Manifold — Curved Surface of Possible States

Every Physics Problem Has a Shape

Imagine a ball inside a bowl. Physics only allows it to be in certain places: on the curved surface. That curved surface is all the states the system can actually reach.

Replace the ball with any physical system. Replace the bowl with physics constraints. The set of all physically possible states forms a curved surface in high-dimensional space — a manifold.

PDEs describe how things move on that surface. But the surface itself is the more fundamental object. If you can learn that surface directly from data, you don't need to derive the PDEs first.

Points far from the manifold are anomalies — physically impossible events. This gives you an anomaly detector grounded in physics, not in labeled examples of past attacks.

🔬 You turn physics into a search problem over priors instead of a derivation problem over equations.

One Architecture, Seven Domains

Change Only the Priors

The same engine handles electrochemistry and Einstein simultaneously. Only the Bayesian priors change — the architecture stays identical.

Battery Management

Real-time EV fleet inference. Detect protocol-valid but physically impossible commands for LFP chemistry.

RF Spectrum

Detect signals inconsistent with known radio propagation physics. Sub-millisecond anomaly scoring.

Network Security

Identify traffic patterns inconsistent with normal operating physics. Physics-grounded anomaly detection.

Gravitational Waves

Kerr waveform surrogate: weeks of supercomputing → <1 second on CPU. 98.5% accuracy retained.

Quantum Gravity

Stress test of universality. GR + QM domains handled by the same architecture. Only priors differ.

Cybersecurity

MW Distance as physics-based anomaly score. Detect what signature-based tools cannot see.

Materials Science

Hypothesis testing without PDEs. Residuals reveal where your material theory needs updating.

Your Domain

If you can describe your system's constraints as priors, MW works. Bring your physics knowledge.

MW Framework vs. Traditional

A Complementary Path, Not a Replacement

PDE methods are mature and powerful — MW offers a different entry point for practitioners who know their domain but not tensor calculus.

Traditional PDE Approach

Requires tensor calculus & differential geometry expertise
Supercomputer needed for complex systems
Re-solving equations for every new condition
High barrier to entry for domain experts
Slow iteration on hypothesis testing
Analytically proven, mathematically rigorous

MW Framework (Manifold Path)

Bayesian priors replace tensor calculus
Runs on CPU — no supercomputer required
Train once, query at millisecond speed (~10,000× faster)
Domain experts can use it directly
Residuals reveal what theory missed automatically
PyTorch + Pyro — standard ML stack

The Residual Is the Finding

In a PDE workflow you would have assumed monotonic battery degradation and moved on. MW shows you exactly where your assumption fails — and by how much.

That 0.41 residual wasn't programmed in. The data pushed back against the assumption. The residual says: something is regenerating charge. Suspect lithium plating or cell reversal.

This is hypothesis testing — done geometrically, without writing a single partial differential equation.

Zenodo Preprint: DOI 10.5281/zenodo.15304813

# Battery EV Fleet — MW Residual Analysis

SOC prior residual: 0.02 ✅ → charge stays in bounds → prior confirmed current prior residual: 0.03 ✅ → current within limits → prior confirmed degradation prior residual: 0.41 ⚠️ → degradation not monotonic in some cells → something is regenerating charge → suspect lithium plating → or cell reversal MW Distance (anomaly score): HIGH → flag for field inspection

Open Source

Our Contributions to the Community

We build in the open. All core frameworks are open source and available on GitHub.

MW Framework

Core engine for physics-AI manifold learning. RF and network security applications. PyTorch + Pyro. No PDEs required.

View on GitHub

Enhanced Agents Framework

Advanced AI agents for cybersecurity automation. Bayesian decision-making built into every agent action.

Learn More

Custom LLM WAF

Web application firewall powered by custom LLM models. Open architecture for enterprise customization.

Learn More

Preprint Available on Zenodo

"339 Years Later: A Physics-AI Path Alternative to Solving PDEs — Modak-Walawalkar Framework" by Rahul Modak & Dr. Rahul Walawalkar (Carnegie Mellon University, NETRA, Caret Capital)

Read the Preprint

Start Thinking in Manifolds

Whether you're a cybersecurity professional, domain expert, or researcher — the MW Framework needs only Python, PyTorch, and Pyro. Install and run in minutes.

Try It on GitHub Contact Our Team

Open Source — MIT License

pip install PyTorch + Pyro

No supercomputer required

No PDE expertise needed