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<title>EMMA — Extracting Multiple physical parameters from Multimodal Data</title>
<meta name="description" content="EMMA: a physics-informed multimodal framework for recovering dynamical parameters from video (with optional audio and chart-image support). CVPR 2026." />
<meta property="og:title" content="EMMA: Extracting Multiple physical parameters from Multimodal Data" />
<meta property="og:description" content="CVPR 2026. Physics-informed parameter recovery from video, with optional audio and plots." />
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<body>

<!-- HEADER -->
<header class="hero">
  <div class="wrap">
    <span class="venue">CVPR 2026</span>
    <h1 class="title"><span class="acronym">EMMA:</span> <em>Extracting Multiple physical parameters from Multimodal Data</em></h1>
    <p class="tldr">Recover the physics of a system from raw video or image, even when the hidden dynamics are unknown.</p>

    <div class="authors-block">
      <ol class="authors">
        <li><a href="https://scholar.google.com/citations?hl=en&amp;user=mbAOSW0AAAAJ" target="_blank" rel="noopener">Farhat Shaikh</a></li>
        <li><a href="https://scholar.google.com/citations?user=UAlc7tEAAAAJ&amp;hl=en" target="_blank" rel="noopener">Ayan Banerjee</a></li>
        <li><a href="https://scholar.google.com/citations?user=U9bcQkMAAAAJ&amp;hl=en" target="_blank" rel="noopener">Sandeep K. S. Gupta</a></li>
      </ol>
      <p class="affil-line">IMPACT Lab, School of Computing &amp; Augmented Intelligence &middot; Arizona State University</p>
      <div class="logo-row" aria-hidden="true">
        <a href="https://impact.lab.asu.edu/" target="_blank" rel="noopener" class="logo-link" aria-label="IMPACT Lab">
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    <div class="actions">
      <a class="btn" href="https://openaccess.thecvf.com/content/CVPR2026/html/Shaikh_EMMA_Extracting_Multiple_physical_parameters_from_Multimodal_Data_CVPR_2026_paper.html" target="_blank" rel="noopener">
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        Video
      </a>
    </div>
  </div>
</header>

<hr class="rule" />

<!-- GALLERY: real footage beside EMMA's simulated trajectory -->
<section id="gallery">
  <div class="wrap">
    <div class="kicker">Gallery</div>
    <h2>Real footage, <span class="em">simulated from recovered parameters.</span></h2>
    <p class="lead">
      For each system, the left panel is the input video; the right panel is a forward
      simulation driven by the physical parameters EMMA recovered from that video.
    </p>

    <div class="gallery">
      <figure class="gtile">
        <figcaption class="gt-label">Pendulum <span>L = 0.86 m, &tau; = 0.045</span></figcaption>
        <div class="gt-bodies">
          <div class="gt-pane"><img src="media/pendulum-real.gif" alt="Real pendulum video" loading="lazy" /><span class="gt-cap">actual</span></div>
          <div class="gt-pane"><img src="media/pendulum-sim.gif" alt="Pendulum simulated from recovered parameters" loading="lazy" /><span class="gt-cap">EMMA</span></div>
        </div>
      </figure>

      <figure class="gtile">
        <figcaption class="gt-label">Free fall <span>g = 9.8 m/s<sup>2</sup></span></figcaption>
        <div class="gt-bodies">
          <div class="gt-pane"><img src="media/free-fall-real.gif" alt="Real free fall video" loading="lazy" /><span class="gt-cap">actual</span></div>
          <div class="gt-pane"><img src="media/free-fall-sim.gif" alt="Free fall simulated from recovered parameters" loading="lazy" /><span class="gt-cap">EMMA</span></div>
        </div>
      </figure>

      <figure class="gtile">
        <figcaption class="gt-label">Torricelli drainage <span>k = 0.0132 &radic;m/s</span></figcaption>
        <div class="gt-bodies">
          <div class="gt-pane"><img src="media/torricelli-real.gif" alt="Real draining container video" loading="lazy" /><span class="gt-cap">actual</span></div>
          <div class="gt-pane"><img src="media/torricelli-sim.gif" alt="Torricelli drainage simulated from recovered parameters" loading="lazy" /><span class="gt-cap">EMMA</span></div>
        </div>
      </figure>

      <figure class="gtile">
        <figcaption class="gt-label">Sliding block <span>&alpha; = 24.7&deg;, &mu; = 0.205</span></figcaption>
        <div class="gt-bodies">
          <div class="gt-pane"><img src="media/sliding-block-real.gif" alt="Real sliding block video" loading="lazy" /><span class="gt-cap">actual</span></div>
          <div class="gt-pane"><img src="media/sliding-block-sim.gif" alt="Sliding block simulated from recovered parameters" loading="lazy" /><span class="gt-cap">EMMA</span></div>
        </div>
      </figure>

      <figure class="gtile">
        <figcaption class="gt-label">LED decay <span>&gamma; = 0.91</span></figcaption>
        <div class="gt-bodies">
          <div class="gt-pane"><img src="media/led-real.gif" alt="Real LED decay video" loading="lazy" /><span class="gt-cap">actual</span></div>
          <div class="gt-pane"><img src="media/led-sim.gif" alt="LED decay simulated from recovered parameters" loading="lazy" /><span class="gt-cap">EMMA</span></div>
        </div>
      </figure>

      <figure class="gtile">
        <figcaption class="gt-label">Rover <span>5 params</span></figcaption>
        <div class="gt-bodies">
          <div class="gt-pane"><img src="media/rover-real.gif" alt="Real differential-drive rover video" loading="lazy" /><span class="gt-cap">actual</span></div>
          <div class="gt-pane"><img src="media/rover-sim.gif" alt="Rover trajectory simulated from recovered parameters" loading="lazy" /><span class="gt-cap">EMMA</span></div>
        </div>
      </figure>

      <figure class="gtile">
        <figcaption class="gt-label">Quadrotor <span>7 params</span></figcaption>
        <div class="gt-bodies">
          <div class="gt-pane"><img src="media/drone-real.gif" alt="Real quadrotor video" loading="lazy" /><span class="gt-cap">actual</span></div>
          <div class="gt-pane"><img src="media/drone-sim.gif" alt="Quadrotor trajectory simulated from recovered parameters" loading="lazy" /><span class="gt-cap">EMMA</span></div>
        </div>
      </figure>
    </div>
  </div>
</section>

<hr class="rule" />

<!-- PITCH / ADVERTISEMENT -->
<section id="pitch">
  <div class="wrap">
    <div class="pitch-head">
      <div class="kicker">Why EMMA</div>
      <h2>Give multimodal data (video, image). <span class="em">EMMA figures out the system.</span></h2>
      <p class="lead" style="margin: 14px auto 0;">
        Point a camera at the system, or hand EMMA a published plot. Provide its
        equation of motion. EMMA recovers the dynamical parameters, the hidden
        actuation, and the coordinate frame, all inside one continuous-time model.
        When audio is available, the same pipeline fuses it with video to resolve
        states that video alone cannot see.
      </p>
    </div>

    <div class="io-panel">
      <div class="io-col">
        <div class="label">You give EMMA</div>
        <h3>A video or a chart, plus the equation of motion.</h3>
        <ul>
          <li><b>Video of the system</b> <span class="tag">visual input</span><br/><span style="color:var(--ink-3);font-size:14px;">raw frames, no masks, no templates</span></li>
          <li><b>Chart images</b> <span class="tag">visual input</span><br/><span style="color:var(--ink-3);font-size:14px;">an alternative to video, for systems known only through published plots</span></li>
          <li><b>Governing ODE form</b> <span class="tag">required</span><br/><span style="color:var(--ink-3);font-size:14px;">the parametric structure of <code>dx/dt = f(x, u; θ)</code> and the parameters you want recovered</span></li>
          <li><b>Audio</b> <span class="tag muted">optional, multimodal</span><br/><span style="color:var(--ink-3);font-size:14px;">paired with video when states or actuation are hidden from the camera</span></li>
        </ul>
      </div>
      <div class="io-col out">
        <div class="label">EMMA returns</div>
        <h3>A calibrated, physics-consistent digital twin.</h3>
        <ul>
          <li><b>Explicit parameters θ</b><br/><span style="color:var(--ink-3);font-size:14px;">mass, length, damping, thrust and torque coefficients, ...</span></li>
          <li><b>Implicit dynamics</b><br/><span style="color:var(--ink-3);font-size:14px;">drag, friction, and other unmeasured physical effects</span></li>
          <li><b>Hidden actuation u(t)</b><br/><span style="color:var(--ink-3);font-size:14px;">latent forcing signals such as wheel speed or rotor rate</span></li>
          <li><b>Calibration invariants</b><br/><span style="color:var(--ink-3);font-size:14px;">coordinate frame, camera alignment, initial state</span></li>
        </ul>
      </div>
    </div>
  </div>
</section>

<hr class="rule" />

<!-- ABSTRACT -->
<section id="abstract">
  <div class="wrap narrow">
    <div class="kicker">Abstract</div>
    <h2>One model, every identifiable parameter.</h2>
    <p class="lead">
      We introduce EMMA, a physics-informed multimodal framework that recovers all
      identifiable dynamical parameters of a system directly from raw video, audio,
      and image-based time-series observations. Unlike prior video-only approaches
      that struggle with occluded states, hidden actuation inputs, or assumptions
      about known initial conditions and coordinate frames, EMMA performs joint
      inference of explicit parameters, implicit dynamical components, and
      calibration invariants within a unified continuous-time model.
    </p>
    <p class="lead" style="margin-top: 14px;">
      Across 100+ scenarios including five standard dynamical benchmarks (75 Delfys
      videos), real-world rover and quadrotor systems with hidden inputs, and
      simulation-chart case studies spanning biological and chaotic systems, EMMA
      delivers robust multi-parameter recovery and significantly outperforms existing
      single-modality and equation-discovery baselines.
    </p>
  </div>
</section>

<hr class="rule" />

<!-- THE PHYSICS (equations) -->
<section id="physics">
  <div class="wrap narrow">
    <div class="kicker">The Physics</div>
    <h2>EMMA needs your equation of motion.</h2>
    <p class="lead">
      EMMA is not data-driven equation discovery. The user supplies the parametric
      structure of the governing ODE; EMMA solves the <em>inverse</em> problem of
      recovering its parameters, along with any latent forcing and invariants, from
      multimodal observations.
    </p>

    <div class="eq-block">
      <div class="eq-row">
        <div>$$ \frac{d\mathbf{x}(t)}{dt} \;=\; f\!\left(\mathbf{x}(t),\,\mathbf{u}(t);\,\boldsymbol{\theta}\right) $$</div>
        <div class="eq-caption">
          For a quadrotor, $\mathbf{x}(t)$ is the drone's state (position and velocity),
          $\mathbf{u}(t)$ is an external input the camera can't see (wind or rotor thrust),
          and $\boldsymbol{\theta}$ is what EMMA recovers (mass, drag, torque).
        </div>
      </div>
    </div>

    <p class="lead" style="margin-top: 22px;">
      EMMA closes the loop with a physics-informed loss: simulate forward using the
      recovered $\boldsymbol{\theta}$, compare to the observed trajectory, and
      backpropagate through the ODE solver until the two agree.
    </p>
  </div>
</section>

<hr class="rule" />

<!-- VIDEO -->
<section id="video">
  <div class="wrap narrow">
    <div class="kicker">Demo</div>
    <h2>Rover, in the lab.</h2>
    <p class="lead">
      Parameter recovery from a differential-drive rover using synchronized video and
      audio. The demo shows the rover scenario only; pendulum, quadrotor, and
      simulation-chart results are covered in the paper.
    </p>
    <a class="yt-card" href="https://youtu.be/Uo79pVlM6Rk" target="_blank" rel="noopener" aria-label="Watch EMMA rover demo on YouTube">
      <img src="emma.png" alt="EMMA demo thumbnail"
           onerror="this.onerror=null;this.src='https://img.youtube.com/vi/Uo79pVlM6Rk/maxresdefault.jpg';" />
      <div class="yt-overlay">
        <div class="yt-play" aria-hidden="true"></div>
        <div class="yt-badge">EMMA &middot; rover demo</div>
      </div>
    </a>
  </div>
</section>

<hr class="rule" />

<!-- METHOD -->
<section id="method">
  <div class="wrap">
    <div class="kicker">Method</div>
    <h2>Three stages, one continuous-time model.</h2>
    <p class="tagline"><span class="em">Sense.</span> <span class="em">Learn.</span> <span class="em">Verify.</span></p>
    <p class="lead">
      EMMA follows a three-step pipeline from raw data to verified parameters. Video
      or chart images are the visual input; audio extends the same pipeline into the
      multimodal setting.
    </p>

    <ol class="stages">
      <li>
        <div class="step-tag">Step 01 &middot; Sense</div>
        <h3>Video &middot; audio &middot; charts</h3>
        <p>Raw modalities are converted into time-aligned signals through modality-specific pipelines.</p>
      </li>
      <li>
        <div class="step-tag">Step 02 &middot; Learn</div>
        <h3>LTC neural network</h3>
        <p>A Liquid Time-Constant network models the system's latent dynamics in continuous time.</p>
      </li>
      <li>
        <div class="step-tag">Step 03 &middot; Verify</div>
        <h3>Physics simulation &amp; loss</h3>
        <p>A differentiable ODE solver simulates the recovered parameters and checks them against the observations.</p>
      </li>
    </ol>

    <figure class="fig" style="margin-top: 28px;">
      <img src="EMMA-arc.png" alt="EMMA architecture: video and audio pipelines feed a shared LTC network and physics-informed digital twin that outputs parameter estimates and a simulated trajectory." />
      <figcaption>
        <b>Figure 1. EMMA architecture.</b> Multimodal inputs (video, audio, image)
        are processed through modality-specific pipelines into unified temporal
        representations. An LTC-NN learns latent dynamics <code>h(t)</code> and
        predicts physical parameters <code>θ</code>. A differentiable physics solver
        validates predictions, enabling end-to-end gradient flow.
      </figcaption>
    </figure>
  </div>
</section>

<hr class="rule" />

<!-- SYSTEMS / EVALUATION -->
<section id="systems">
  <div class="wrap">
    <div class="kicker">Evaluation</div>
    <h2>Across benchmarks, hardware, and simulation charts.</h2>
    <p class="lead">
      EMMA is evaluated on five canonical video benchmarks, real-world platforms with
      hidden forcing, and chart-based simulation studies spanning biological and
      chaotic regimes.
    </p>

    <div class="res-grid">
      <div class="res-card">
        <div class="res-num">8.8<span>%</span> &plusmn;&nbsp;1.7%</div>
        <div class="res-label">mean error</div>
        <div class="res-note"><em>Rover (5 params)</em></div>
      </div>
      <div class="res-card">
        <div class="res-num">100<span>+</span> scenarios</div>
        <div class="res-label">Delfys benchmark, rover, drone</div>
        <div class="res-note"><em>&amp; simulation charts</em></div>
      </div>
      <div class="res-card">
        <div class="res-num">&gt; 10<span>&times;</span> lower</div>
        <div class="res-label">implicit RMSE</div>
        <div class="res-note"><em>vs PySINDy</em></div>
      </div>
      <div class="res-card">
        <div class="res-num">107<span>&times;</span> smaller</div>
        <div class="res-label">compact model</div>
        <div class="res-note"><em>vs Delfys baseline</em></div>
      </div>
    </div>

    <p class="lead" style="margin: 28px 0 0;">
      Compared against <b>PAIG</b>, <b>NIRPI</b>, and <b>Delfys</b> on the video benchmarks
      and <b>PySINDy</b> on the chart-based simulations. Rover and quadrotor under hidden
      forcing are reported as first-of-their-kind results. Full tables, ablations, and
      per-system comparisons are in the <a href="https://openaccess.thecvf.com/content/CVPR2026/html/Shaikh_EMMA_Extracting_Multiple_physical_parameters_from_Multimodal_Data_CVPR_2026_paper.html" target="_blank" rel="noopener">paper</a>.
    </p>

    <h3 class="eval-sub">Supported systems</h3>
    <div class="sys-grid">
      <div class="sys-card">
        <div class="cat">Delfys Benchmark</div>
        <ul>
          <li>Pendulum</li>
          <li>Torricelli drainage</li>
          <li>Sliding block</li>
          <li>LED decay</li>
          <li>Free fall</li>
        </ul>
      </div>
      <div class="sys-card">
        <div class="cat">Real-world platforms</div>
        <ul>
          <li>Differential-drive rover</li>
          <li>6-DoF quadrotor</li>
          <li>Hidden audio forcing</li>
        </ul>
      </div>
      <div class="sys-card">
        <div class="cat">Simulation charts</div>
        <ul>
          <li>Lotka-Volterra</li>
          <li>Chaotic Lorenz</li>
          <li>F8 Crusader</li>
          <li>HIV therapy</li>
          <li>AID (Type-1 diabetes)</li>
        </ul>
      </div>
    </div>

  </div>
</section>

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    <div class="kicker">Citation</div>
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<pre class="bibtex" id="bibtex-source"><span class="k">@InProceedings</span>{Shaikh_2026_CVPR,
  <span class="k">author</span>    = <span class="v">{Shaikh, Farhat and Banerjee, Ayan and Gupta, Sandeep}</span>,
  <span class="k">title</span>     = <span class="v">{EMMA: Extracting Multiple physical parameters from Multimodal Data}</span>,
  <span class="k">booktitle</span> = <span class="v">{Proceedings of the IEEE/CVF Conference on Computer Vision
               and Pattern Recognition (CVPR)}</span>,
  <span class="k">month</span>     = <span class="v">{June}</span>,
  <span class="k">year</span>      = <span class="v">{2026}</span>,
  <span class="k">pages</span>     = <span class="v">{1716-1725}</span>
}</pre>
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      <div>IMPACT Lab, Arizona State University</div>
      <div style="display: flex; gap: 20px;">
        <a href="https://github.com/ImpactLabASU/EMMA-CVPR2026" target="_blank" rel="noopener">GitHub</a>
        <span>Paper:
          <a href="https://openaccess.thecvf.com/content/CVPR2026/html/Shaikh_EMMA_Extracting_Multiple_physical_parameters_from_Multimodal_Data_CVPR_2026_paper.html" target="_blank" rel="noopener">CVF</a>,
          <a href="https://arxiv.org/abs/2605.24047" target="_blank" rel="noopener">arXiv</a>
        </span>
        <a href="#citation">BibTeX</a>
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    <div class="ack">
      <strong style="color: var(--ink);">Acknowledgments.</strong> Partially funded by
      DARPA AMP (N6600120C4020), DARPA FIRE (P000050426), NSF FDT-Biotech (2436801),
      and NIH R21 (1R21HL175632).
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